diff --git a/tests/unit/executor/test_api.py b/tests/unit/executor/test_api.py
index 2b9a5d52..160c79f6 100644
--- a/tests/unit/executor/test_api.py
+++ b/tests/unit/executor/test_api.py
@@ -119,6 +119,23 @@ def test_empty(self):
         cache_lst = get_cache_data(cache_directory="rather_this_dir")
         self.assertEqual(len(cache_lst), 1)
 
+    def test_executor_dependencies(self):
+        with TestClusterExecutor(cache_directory="cache_dir") as exe:
+            cloudpickle_register(ind=1)
+            fs1 = exe.submit(add_with_sleep, 1, 1)
+            fs2 = exe.submit(add_with_sleep, fs1, 1)
+            fs3 = exe.submit(add_with_sleep, fs1, fs2)
+            self.assertFalse(fs1.done())
+            self.assertFalse(fs2.done())
+            self.assertFalse(fs3.done())
+            self.assertEqual(fs1.result(), 2)
+            self.assertEqual(fs2.result(), 3)
+            self.assertEqual(fs3.result(), 5)
+            self.assertEqual(len(os.listdir("cache_dir")), 3)
+            self.assertTrue(fs1.done())
+            self.assertTrue(fs2.done())
+            self.assertTrue(fs3.done())
+
     def test_executor_dependency_plot(self):
         with TestClusterExecutor(
             plot_dependency_graph=True,
diff --git a/tests/unit/executor/test_flux_cluster.py b/tests/unit/executor/test_flux_cluster.py
index 57b58f2c..37661b13 100644
--- a/tests/unit/executor/test_flux_cluster.py
+++ b/tests/unit/executor/test_flux_cluster.py
@@ -47,6 +47,11 @@ def stop_function():
     return True
 
 
+def add_with_sleep(parameter_1, parameter_2):
+    sleep(1)
+    return parameter_1 + parameter_2
+
+
 @unittest.skipIf(
     skip_flux_test or skip_mpi4py_test,
     "h5py or mpi4py or flux are not installed, so the h5py, flux and mpi4py tests are skipped.",
@@ -81,6 +86,27 @@ def test_executor_blockallocation(self):
             self.assertEqual(len(os.listdir("executorlib_cache")), 2)
             self.assertTrue(fs1.done())
 
+    def test_executor_dependencies(self):
+        with FluxClusterExecutor(
+            resource_dict={"cores": 1, "cwd": "executorlib_cache"},
+            block_allocation=False,
+            cache_directory="executorlib_cache",
+            pmi_mode=pmi,
+        ) as exe:
+            fs1 = exe.submit(add_with_sleep, 1, 1)
+            fs2 = exe.submit(add_with_sleep, fs1, 1)
+            fs3 = exe.submit(add_with_sleep, fs1, fs2)
+            self.assertFalse(fs1.done())
+            self.assertFalse(fs2.done())
+            self.assertFalse(fs3.done())
+            self.assertEqual(fs1.result(), 2)
+            self.assertEqual(fs2.result(), 3)
+            self.assertEqual(fs3.result(), 5)
+            self.assertEqual(len(os.listdir("executorlib_cache")), 6)
+            self.assertTrue(fs1.done())
+            self.assertTrue(fs2.done())
+            self.assertTrue(fs3.done())
+
     def test_executor_blockallocation_echo(self):
         with FluxClusterExecutor(
             resource_dict={"cores": 1, "cwd": "executorlib_cache"},
diff --git a/tests/unit/executor/test_slurm_cluster.py b/tests/unit/executor/test_slurm_cluster.py
index 41057119..feccf2f0 100644
--- a/tests/unit/executor/test_slurm_cluster.py
+++ b/tests/unit/executor/test_slurm_cluster.py
@@ -2,6 +2,7 @@
 import importlib
 import unittest
 import shutil
+from time import sleep
 
 from executorlib import SlurmClusterExecutor
 from executorlib.standalone.serialize import cloudpickle_register
@@ -34,6 +35,9 @@
 #SBATCH --chdir={{working_directory}}
 #SBATCH --get-user-env=L
 #SBATCH --ntasks={{cores}}
+{%- if dependency_list %}
+#SBATCH --dependency=afterok:{{ dependency_list | join(',') }}
+{%- endif %}
 
 {{command}}
 """
@@ -47,6 +51,11 @@ def mpi_funct(i):
     return i, size, rank
 
 
+def add_with_sleep(parameter_1, parameter_2):
+    sleep(1)
+    return parameter_1 + parameter_2
+
+
 @unittest.skipIf(
     skip_slurm_test or skip_mpi4py_test or skip_h5py_test,
     "h5py or mpi4py or SLRUM are not installed, so the h5py, slurm and mpi4py tests are skipped.",
@@ -66,6 +75,27 @@ def test_executor(self):
             self.assertEqual(len(os.listdir("executorlib_cache")), 3)
             self.assertTrue(fs1.done())
 
+    def test_executor_dependencies(self):
+        with SlurmClusterExecutor(
+            resource_dict={"cores": 1, "cwd": "executorlib_cache", "submission_template": submission_template},
+            block_allocation=False,
+            cache_directory="executorlib_cache",
+            pmi_mode="pmi2",
+        ) as exe:
+            fs1 = exe.submit(add_with_sleep, 1, 1)
+            fs2 = exe.submit(add_with_sleep, fs1, 1)
+            fs3 = exe.submit(add_with_sleep, fs1, fs2)
+            self.assertFalse(fs1.done())
+            self.assertFalse(fs2.done())
+            self.assertFalse(fs3.done())
+            self.assertEqual(fs1.result(), 2)
+            self.assertEqual(fs2.result(), 3)
+            self.assertEqual(fs3.result(), 5)
+            self.assertEqual(len(os.listdir("executorlib_cache")), 5)
+            self.assertTrue(fs1.done())
+            self.assertTrue(fs2.done())
+            self.assertTrue(fs3.done())
+
     def test_executor_no_cwd(self):
         with SlurmClusterExecutor(
             resource_dict={"cores": 2, "submission_template": submission_template},