diff --git a/devito/core/cpu.py b/devito/core/cpu.py
index 81611da9b4..1d34314697 100644
--- a/devito/core/cpu.py
+++ b/devito/core/cpu.py
@@ -6,8 +6,9 @@
 from devito.passes.clusters import (Lift, blocking, buffering, cire, cse,
                                     factorize, fission, fuse, optimize_pows,
                                     optimize_hyperplanes)
-from devito.passes.iet import (CTarget, OmpTarget, avoid_denormals, linearize, mpiize,
-                               hoist_prodders, relax_incr_dimensions)
+from devito.passes.iet import (CTarget, OmpTarget, avoid_denormals, linearize,
+                               mpiize, hoist_prodders, relax_incr_dimensions,
+                               check_stability)
 from devito.tools import timed_pass
 
 __all__ = ['Cpu64NoopCOperator', 'Cpu64NoopOmpOperator', 'Cpu64AdvCOperator',
@@ -76,6 +77,7 @@ def _normalize_kwargs(cls, **kwargs):
         o['mapify-reduce'] = oo.pop('mapify-reduce', cls.MAPIFY_REDUCE)
         o['index-mode'] = oo.pop('index-mode', cls.INDEX_MODE)
         o['place-transfers'] = oo.pop('place-transfers', True)
+        o['errctl'] = oo.pop('errctl', cls.ERRCTL)
 
         # Recognised but unused by the CPU backend
         oo.pop('par-disabled', None)
@@ -189,6 +191,9 @@ def _specialize_iet(cls, graph, **kwargs):
         # Misc optimizations
         hoist_prodders(graph)
 
+        # Perform error checking
+        check_stability(graph, **kwargs)
+
         # Symbol definitions
         cls._Target.DataManager(**kwargs).process(graph)
 
diff --git a/devito/core/gpu.py b/devito/core/gpu.py
index de070c6890..a0c2da774a 100644
--- a/devito/core/gpu.py
+++ b/devito/core/gpu.py
@@ -10,8 +10,9 @@
 from devito.passes.clusters import (Lift, Streaming, Tasker, blocking, buffering,
                                     cire, cse, factorize, fission, fuse,
                                     optimize_pows)
-from devito.passes.iet import (DeviceOmpTarget, DeviceAccTarget, mpiize, hoist_prodders,
-                               linearize, pthreadify, relax_incr_dimensions)
+from devito.passes.iet import (DeviceOmpTarget, DeviceAccTarget, mpiize,
+                               hoist_prodders, linearize, pthreadify,
+                               relax_incr_dimensions, check_stability)
 from devito.tools import as_tuple, timed_pass
 
 __all__ = ['DeviceNoopOperator', 'DeviceAdvOperator', 'DeviceCustomOperator',
@@ -91,6 +92,7 @@ def _normalize_kwargs(cls, **kwargs):
         o['mapify-reduce'] = oo.pop('mapify-reduce', cls.MAPIFY_REDUCE)
         o['index-mode'] = oo.pop('index-mode', cls.INDEX_MODE)
         o['place-transfers'] = oo.pop('place-transfers', True)
+        o['errctl'] = oo.pop('errctl', cls.ERRCTL)
 
         if oo:
             raise InvalidOperator("Unsupported optimization options: [%s]"
@@ -226,6 +228,9 @@ def _specialize_iet(cls, graph, **kwargs):
         # Misc optimizations
         hoist_prodders(graph)
 
+        # Perform error checking
+        check_stability(graph, **kwargs)
+
         # Symbol definitions
         cls._Target.DataManager(**kwargs).process(graph)
 
diff --git a/devito/core/operator.py b/devito/core/operator.py
index 1ba976d3b6..e61ff2c806 100644
--- a/devito/core/operator.py
+++ b/devito/core/operator.py
@@ -119,6 +119,13 @@ class BasicOperator(Operator):
     (default) or `int32`.
     """
 
+    ERRCTL = None
+    """
+    Runtime error checking. If this option is enabled, the generated code will
+    include runtime checks for various things that might go south, such as
+    instability (e.g., NaNs), failed library calls (e.g., kernel launches).
+    """
+
     _Target = None
     """
     The target language constructor, to be specified by subclasses.
@@ -155,6 +162,9 @@ def _check_kwargs(cls, **kwargs):
         if oo['deriv-unroll'] not in (False, 'inner', 'full'):
             raise InvalidArgument("Illegal `deriv-unroll` value")
 
+        if oo['errctl'] not in (None, False, 'basic', 'max'):
+            raise InvalidArgument("Illegal `errctl` value")
+
     def _autotune(self, args, setup):
         if setup in [False, 'off']:
             return args
diff --git a/devito/exceptions.py b/devito/exceptions.py
index f03b0720ec..fa5619d4ca 100644
--- a/devito/exceptions.py
+++ b/devito/exceptions.py
@@ -14,5 +14,9 @@ class InvalidOperator(DevitoError):
     pass
 
 
+class ExecutionError(DevitoError):
+    pass
+
+
 class VisitorException(DevitoError):
     pass
diff --git a/devito/ir/iet/nodes.py b/devito/ir/iet/nodes.py
index 72307c5ac5..36a7a2f836 100644
--- a/devito/ir/iet/nodes.py
+++ b/devito/ir/iet/nodes.py
@@ -794,17 +794,19 @@ class CallableBody(MultiTraversable):
         Data unbundling for `body`.
     frees : list of Calls, optional
         Data deallocations for `body`.
+    errors : list of Nodes, optional
+        Error handling for `body`.
     """
 
     is_CallableBody = True
 
     _traversable = ['unpacks', 'init', 'standalones', 'allocs', 'stacks',
                     'casts', 'bundles', 'maps', 'strides', 'objs', 'body',
-                    'unmaps', 'unbundles', 'frees']
+                    'unmaps', 'unbundles', 'frees', 'errors']
 
     def __init__(self, body, init=(), standalones=(), unpacks=(), strides=(),
                  allocs=(), stacks=(), casts=(), bundles=(), objs=(), maps=(),
-                 unmaps=(), unbundles=(), frees=()):
+                 unmaps=(), unbundles=(), frees=(), errors=()):
         # Sanity check
         assert not isinstance(body, CallableBody), "CallableBody's cannot be nested"
 
@@ -823,6 +825,7 @@ def __init__(self, body, init=(), standalones=(), unpacks=(), strides=(),
         self.unmaps = as_tuple(unmaps)
         self.unbundles = as_tuple(unbundles)
         self.frees = as_tuple(frees)
+        self.errors = as_tuple(errors)
 
     def __repr__(self):
         return ("<CallableBody <unpacks=%d, allocs=%d, casts=%d, maps=%d, "
diff --git a/devito/operator/operator.py b/devito/operator/operator.py
index df03ca7653..45860303e8 100644
--- a/devito/operator/operator.py
+++ b/devito/operator/operator.py
@@ -8,7 +8,7 @@
 
 from devito.arch import compiler_registry, platform_registry
 from devito.data import default_allocator
-from devito.exceptions import InvalidOperator
+from devito.exceptions import InvalidOperator, ExecutionError
 from devito.logger import debug, info, perf, warning, is_log_enabled_for
 from devito.ir.equations import LoweredEq, lower_exprs
 from devito.ir.clusters import ClusterGroup, clusterize
@@ -21,7 +21,8 @@
 from devito.mpi import MPI
 from devito.parameters import configuration
 from devito.passes import (Graph, lower_index_derivatives, generate_implicit,
-                           generate_macros, minimize_symbols, unevaluate)
+                           generate_macros, minimize_symbols, unevaluate,
+                           error_mapper)
 from devito.symbolics import estimate_cost
 from devito.tools import (DAG, OrderedSet, Signer, ReducerMap, as_tuple, flatten,
                           filter_sorted, frozendict, is_integer, split, timed_pass,
@@ -646,6 +647,16 @@ def _prepare_arguments(self, autotune=None, **kwargs):
 
         return args
 
+    def _postprocess_errors(self, retval):
+        if retval == 0:
+            return
+        elif retval == error_mapper['Stability']:
+            raise ExecutionError("Detected nan/inf in some output Functions")
+        elif retval == error_mapper['KernelLaunch']:
+            raise ExecutionError("Kernel launch failed")
+        else:
+            raise ExecutionError("An error occurred during execution")
+
     def _postprocess_arguments(self, args, **kwargs):
         """Process runtime arguments upon returning from ``.apply()``."""
         for p in self.parameters:
@@ -842,7 +853,7 @@ def apply(self, **kwargs):
         try:
             cfunction = self.cfunction
             with self._profiler.timer_on('apply', comm=args.comm):
-                cfunction(*arg_values)
+                retval = cfunction(*arg_values)
         except ctypes.ArgumentError as e:
             if e.args[0].startswith("argument "):
                 argnum = int(e.args[0][9:].split(':')[0]) - 1
@@ -854,6 +865,9 @@ def apply(self, **kwargs):
             else:
                 raise
 
+        # Perform error checking
+        self._postprocess_errors(retval)
+
         # Post-process runtime arguments
         self._postprocess_arguments(args, **kwargs)
 
diff --git a/devito/passes/iet/__init__.py b/devito/passes/iet/__init__.py
index 7ba70e2930..c09db00c9b 100644
--- a/devito/passes/iet/__init__.py
+++ b/devito/passes/iet/__init__.py
@@ -7,3 +7,4 @@
 from .asynchrony import *  # noqa
 from .instrument import *  # noqa
 from .languages import *  # noqa
+from .errors import *  # noqa
diff --git a/devito/passes/iet/errors.py b/devito/passes/iet/errors.py
new file mode 100644
index 0000000000..a6785f170b
--- /dev/null
+++ b/devito/passes/iet/errors.py
@@ -0,0 +1,87 @@
+import cgen as c
+import numpy as np
+from sympy import Not
+
+from devito.ir.iet import (Call, Conditional, EntryFunction, Iteration, List,
+                           Return, FindNodes, FindSymbols, Transformer,
+                           make_callable)
+from devito.passes.iet.engine import iet_pass
+from devito.symbolics import CondEq, DefFunction
+from devito.types import Eq, Inc, Symbol
+
+__all__ = ['check_stability', 'error_mapper']
+
+
+def check_stability(graph, options=None, rcompile=None, sregistry=None, **kwargs):
+    """
+    Check if the simulation is stable. If not, return to Python as quickly as
+    possible with an error code.
+    """
+    if options['errctl'] != 'max':
+        return
+
+    _, wmovs = graph.data_movs
+
+    _check_stability(graph, wmovs=wmovs, rcompile=rcompile, sregistry=sregistry)
+
+
+@iet_pass
+def _check_stability(iet, wmovs=(), rcompile=None, sregistry=None):
+    if not isinstance(iet, EntryFunction):
+        return iet, {}
+
+    # NOTE: Stability is a domain-specific concept, hence looking for time
+    # Iterations and TimeFunctions is acceptable
+    efuncs = []
+    includes = []
+    mapper = {}
+    for n in FindNodes(Iteration).visit(iet):
+        if not n.dim.is_Time:
+            continue
+
+        functions = [f for f in FindSymbols().visit(n)
+                     if f.is_TimeFunction and f.time_dim.is_Stepping]
+
+        # We compute the norm of just one TimeFunction, hence we sort for
+        # determinism and reproducibility
+        candidates = sorted(set(functions) & set(wmovs), key=lambda f: f.name)
+        for f in candidates:
+            if f in wmovs:
+                break
+        else:
+            continue
+
+        accumulator = Symbol(name='accumulator', dtype=f.dtype)
+        eqns = [Eq(accumulator, 0.0),
+                Inc(accumulator, f.subs(f.time_dim, 0))]
+        irs, byproduct = rcompile(eqns)
+
+        name = sregistry.make_name(prefix='is_finite')
+        retval = Return(DefFunction('isfinite', accumulator))
+        body = irs.iet.body.body + (retval,)
+        efunc = make_callable(name, body, retval='int')
+
+        efuncs.extend([i.root for i in byproduct.funcs])
+        efuncs.append(efunc)
+
+        includes.extend(byproduct.includes)
+
+        name = sregistry.make_name(prefix='check')
+        check = Symbol(name=name, dtype=np.int32)
+
+        errctl = Conditional(CondEq(n.dim % 100, 0), List(body=[
+            Call(efunc.name, efunc.parameters, retobj=check),
+            Conditional(Not(check), Return(error_mapper['Stability']))
+        ]))
+        errctl = List(header=c.Comment("Stability check"), body=[errctl])
+        mapper[n] = n._rebuild(nodes=n.nodes + (errctl,))
+
+    iet = Transformer(mapper).visit(iet)
+
+    return iet, {'efuncs': efuncs, 'includes': includes}
+
+
+error_mapper = {
+    'Stability': 100,
+    'KernelLaunch': 200,
+}
diff --git a/tests/test_error_checking.py b/tests/test_error_checking.py
new file mode 100644
index 0000000000..061cb2b575
--- /dev/null
+++ b/tests/test_error_checking.py
@@ -0,0 +1,27 @@
+import pytest
+
+from devito import Grid, Function, TimeFunction, Eq, Operator, switchconfig
+from devito.exceptions import ExecutionError
+
+
+@switchconfig(safe_math=True)
+@pytest.mark.parametrize("expr", [
+    'u/f',
+    '(u + v)/f',
+])
+def test_stability(expr):
+    grid = Grid(shape=(10, 10))
+
+    f = Function(name='f', grid=grid, space_order=2)  # noqa
+    u = TimeFunction(name='u', grid=grid, space_order=2)
+    v = TimeFunction(name='v', grid=grid, space_order=2)
+
+    eq = Eq(u.forward, eval(expr))
+
+    op = Operator(eq, opt=('advanced', {'errctl': 'max'}))
+
+    u.data[:] = 1.
+    v.data[:] = 2.
+
+    with pytest.raises(ExecutionError):
+        op.apply(time_M=200, dt=.1)