diff --git a/ggml/src/ggml-cuda.cu b/ggml/src/ggml-cuda.cu
index e4bd77ca6..c5ca7aef1 100644
--- a/ggml/src/ggml-cuda.cu
+++ b/ggml/src/ggml-cuda.cu
@@ -2885,6 +2885,8 @@ GGML_CALL static bool ggml_backend_cuda_supports_op(ggml_backend_t backend, cons
         case GGML_OP_ARANGE:
         case GGML_OP_TIMESTEP_EMBEDDING:
         case GGML_OP_LEAKY_RELU:
+        case GGML_OP_SSM_CONV:
+        case GGML_OP_SSM_SCAN:
             return true;
         case GGML_OP_FLASH_ATTN_EXT:
 #if defined(GGML_USE_HIPBLAS) && defined(__HIP_PLATFORM_AMD__)
diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 351b1d567..ddcc2cb6e 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -1642,6 +1642,76 @@ struct test_leaky_relu : public test_case {
     }
 };
 
+// GGML_OP_SSM_CONV
+struct test_ssm_conv : public test_case {
+    const ggml_type type;
+
+    std::string vars() override {
+        return VARS_TO_STR4(type, 3, 1536, 4);
+    }
+
+    test_ssm_conv(ggml_type type = GGML_TYPE_F32)
+        : type(type) {}
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        ggml_tensor * s = ggml_new_tensor_3d(ctx, type, 3, 1536, 1);
+        ggml_tensor * x = ggml_new_tensor_2d(ctx, type, 1536, 1);
+        ggml_tensor * c = ggml_new_tensor_2d(ctx, type, 4, 1536);
+        ggml_tensor * sq = ggml_new_tensor_2d(ctx, GGML_TYPE_I32, 1, 1);
+        ggml_tensor * out = ggml_ssm_conv(ctx, s, x, c, sq);
+        return out;
+    }
+
+    void initialize_tensors(ggml_context * ctx) override {
+        for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
+            if (t->type == GGML_TYPE_I32) {
+                std::vector<int> data(1);
+                data[0] = 0;
+                ggml_backend_tensor_set(t, data.data(), 0, 1 * sizeof(int));
+            } else {
+                init_tensor_uniform(t);
+            }
+        }
+    }
+};
+
+// GGML_OP_SSM_SCAN
+struct test_ssm_scan : public test_case {
+    const ggml_type type;
+
+    std::string vars() override {
+        return VARS_TO_STR4(type, 16, 1536, 2);
+    }
+
+    test_ssm_scan(ggml_type type = GGML_TYPE_F32)
+        : type(type) {}
+
+    ggml_tensor * build_graph(ggml_context * ctx) override {
+        ggml_tensor * s = ggml_new_tensor_3d(ctx, type, 16, 1536, 1);
+        ggml_tensor * x = ggml_new_tensor_2d(ctx, type, 1536, 2);
+        ggml_tensor * dt = ggml_new_tensor_2d(ctx, type, 1536, 2);
+        ggml_tensor * A = ggml_new_tensor_2d(ctx, type, 16, 1536);
+        ggml_tensor * B = ggml_new_tensor_2d(ctx, type, 16, 2);
+        ggml_tensor * C = ggml_new_tensor_2d(ctx, type, 16, 2);
+        ggml_tensor * sq = ggml_new_tensor_2d(ctx, GGML_TYPE_I32, 1, 2);
+        ggml_tensor * out = ggml_ssm_scan(ctx, s, x, dt, A, B, C, sq);
+        return out;
+    }
+
+    void initialize_tensors(ggml_context * ctx) override {
+        for (ggml_tensor * t = ggml_get_first_tensor(ctx); t != NULL; t = ggml_get_next_tensor(ctx, t)) {
+            if (t->type == GGML_TYPE_I32) {
+                std::vector<int> data(2);
+                data[0] = 0;
+                data[1] = 0;
+                ggml_backend_tensor_set(t, data.data(), 0, 2 * sizeof(int));
+            } else {
+                init_tensor_uniform(t);
+            }
+        }
+    }
+};
+
 // GGML_OP_FLASH_ATTN_EXT
 struct test_flash_attn_ext : public test_case {
     const int64_t hs; // head size
@@ -2433,6 +2503,8 @@ static bool test_backend(ggml_backend_t backend, test_mode mode, const char * op
     test_cases.emplace_back(new test_arange());
     test_cases.emplace_back(new test_timestep_embedding());
     test_cases.emplace_back(new test_leaky_relu());
+    test_cases.emplace_back(new test_ssm_conv());
+    test_cases.emplace_back(new test_ssm_scan());
 
     for (int hs : { 64, 80, 128, 256, }) {
         for (bool mask : { true, false } ) {