diff --git a/gap/digraph.gd b/gap/digraph.gd
index 8c3924bc6..d93389b46 100644
--- a/gap/digraph.gd
+++ b/gap/digraph.gd
@@ -14,6 +14,7 @@ DeclareCategory("IsDigraphWithAdjacencyFunction", IsDigraph);
 DeclareCategory("IsCayleyDigraph", IsDigraph);
 DeclareCategory("IsImmutableDigraph", IsDigraph);
 DeclareSynonym("IsMutableDigraph", IsDigraph and IsMutable);
+DeclareCategoryCollections("IsDigraph");
 
 DeclareAttribute("DigraphMutabilityFilter", IsDigraph);
 
diff --git a/gap/oper.gd b/gap/oper.gd
index e8fa1f176..45c48ea3c 100644
--- a/gap/oper.gd
+++ b/gap/oper.gd
@@ -59,6 +59,8 @@ DeclareOperation("DIGRAPHS_GraphProduct", [IsDigraph, IsDigraph, IsFunction]);
 # 4. Actions . . .
 DeclareOperation("OnDigraphs", [IsDigraph, IsPerm]);
 DeclareOperation("OnDigraphs", [IsDigraph, IsTransformation]);
+DeclareOperation("OnTuplesDigraphs", [IsDigraphCollection, IsPerm]);
+DeclareOperation("OnSetsDigraphs", [IsDigraphCollection, IsPerm]);
 DeclareOperation("OnMultiDigraphs", [IsDigraph, IsPermCollection]);
 DeclareOperation("OnMultiDigraphs", [IsDigraph, IsPerm, IsPerm]);
 
diff --git a/gap/oper.gi b/gap/oper.gi
index 7ee4ef858..b50fd22cf 100644
--- a/gap/oper.gi
+++ b/gap/oper.gi
@@ -826,6 +826,18 @@ function(D, t)
   return MakeImmutable(OnDigraphs(DigraphMutableCopy(D), t));
 end);
 
+# TODO DigraphByOutNeighboursColl
+InstallMethod(OnTuplesDigraphs,
+"for list of digraphs and a perm",
+[IsDigraphCollection and IsList, IsPerm],
+{L, p} -> List(L, D -> OnDigraphs(D, p)));
+
+# TODO DigraphByOutNeighboursColl
+InstallMethod(OnSetsDigraphs,
+"for a set of digraphs and a perm",
+[IsDigraphCollection and IsSet, IsPerm],
+{S, p} -> Set(S, D -> OnDigraphs(D, p)));
+
 # Not revising the following because multi-digraphs are being withdrawn in the
 # near future.
 
diff --git a/tst/standard/oper.tst b/tst/standard/oper.tst
index f9bf07118..85b3ce0a6 100644
--- a/tst/standard/oper.tst
+++ b/tst/standard/oper.tst
@@ -149,6 +149,31 @@ gap> gr := OnDigraphs(gr, t);
 gap> OutNeighbours(gr);
 [ [ 2 ], [ 1, 1 ], [  ] ]
 
+#  OnTuplesDigraphs: for a digraph and a permutation
+gap> D := [ChainDigraph(3), CycleDigraph(4)];;
+gap> List(D, OutNeighbours);
+[ [ [ 2 ], [ 3 ], [  ] ], [ [ 2 ], [ 3 ], [ 4 ], [ 1 ] ] ]
+gap> List(OnTuplesDigraphs(D, (1, 3)), OutNeighbours);
+[ [ [  ], [ 1 ], [ 2 ] ], [ [ 4 ], [ 1 ], [ 2 ], [ 3 ] ] ]
+gap> D := [ChainDigraph(3), DigraphReverse(ChainDigraph(3))];;
+gap> List(D, OutNeighbours);
+[ [ [ 2 ], [ 3 ], [  ] ], [ [  ], [ 1 ], [ 2 ] ] ]
+gap> List(OnTuplesDigraphs(D, (1, 3)), OutNeighbours);
+[ [ [  ], [ 1 ], [ 2 ] ], [ [ 2 ], [ 3 ], [  ] ] ]
+gap> OnTuplesDigraphs(D, (1, 3)) = Permuted(D, (1, 2));
+true
+
+#  OnSetsDigraphs: for a digraph and a permutation
+gap> D := [ChainDigraph(3), DigraphReverse(ChainDigraph(3))];;
+gap> IsSet(D);
+true
+gap> OnSetsDigraphs(D, (1, 3)) = D;
+true
+gap> OnSetsDigraphs(D, (1, 3)) = OnTuplesDigraphs(D, (1, 3));
+false
+gap> MinimalGeneratingSet(Stabilizer(SymmetricGroup(3), D, OnSetsDigraphs));
+[ (1,3) ]
+
 #  OnMultiDigraphs: for a pair of permutations
 gap> gr1 := CompleteDigraph(3);
 <immutable complete digraph with 3 vertices>