diff --git a/loopy/library/reduction.py b/loopy/library/reduction.py
index 8e32e417038f669b7306eda664a4f4dd12255ce1..ac749f6eff8b7e12b2376e916066218f76e4ebd2 100644
--- a/loopy/library/reduction.py
+++ b/loopy/library/reduction.py
@@ -188,8 +188,15 @@ def get_le_neutral(dtype):
         elif dtype.numpy_dtype.itemsize == 8:
             # 64 bit integer
             return var("LONG_MAX")
-    else:
-        raise NotImplementedError("less")
+    elif dtype.numpy_dtype.kind == "u":
+        if dtype.numpy_dtype.itemsize == 4:
+            # 32 bit integer
+            return var("UINT_MAX")
+        elif dtype.numpy_dtype.itemsize == 8:
+            # 64 bit integer
+            return var("ULONG_MAX")
+
+    raise NotImplementedError(f"neutral element for <= and {dtype}")
 
 
 def get_ge_neutral(dtype):
@@ -211,8 +218,10 @@ def get_ge_neutral(dtype):
         elif dtype.numpy_dtype.itemsize == 8:
             # 64 bit integer
             return var("LONG_MIN")
-    else:
-        raise NotImplementedError("less")
+    elif dtype.numpy_dtype.kind == "u":
+        return 0
+
+    raise NotImplementedError(f"neutral element for >= and {dtype}")
 
 
 class MaxReductionOperation(ScalarReductionOperation):