diff --git a/conda/recipes/rmm/meta.yaml b/conda/recipes/rmm/meta.yaml
index b3457d922..477927e27 100644
--- a/conda/recipes/rmm/meta.yaml
+++ b/conda/recipes/rmm/meta.yaml
@@ -53,10 +53,10 @@ requirements:
     - cuda-version ={{ cuda_version }}
     {% if cuda_major == "11" %}
     - cudatoolkit
-    - cuda-python ==11.7.1
+    - cuda-python >=11.7.1,<12.0a0
     {% else %}
     - cuda-cudart-dev
-    - cuda-python ==12.0.0
+    - cuda-python >=12.0,<13.0a0
     {% endif %}
     - cython >=3.0.0
     - librmm ={{ version }}