diff --git a/tests/metrics/test_composition.py b/tests/metrics/test_composition.py
index 087dee521d6941..a9bba7d7fac7da 100644
--- a/tests/metrics/test_composition.py
+++ b/tests/metrics/test_composition.py
@@ -1,3 +1,4 @@
+from distutils.version import LooseVersion
 from operator import neg, pos
 
 import pytest
@@ -6,6 +7,11 @@
 from pytorch_lightning.metrics.compositional import CompositionalMetric
 from pytorch_lightning.metrics.metric import Metric
 
+_MARK_TORCH_LOWER_1_4 = dict(condition=LooseVersion(torch.__version__) < LooseVersion("1.5.0"),
+                             reason='required PT >= 1.5')
+_MARK_TORCH_LOWER_1_5 = dict(condition=LooseVersion(torch.__version__) < LooseVersion("1.6.0"),
+                             reason='required PT >= 1.6')
+
 
 class DummyMetric(Metric):
     def __init__(self, val_to_return):
@@ -50,6 +56,7 @@ def test_metrics_add(second_operand, expected_result):
     ["second_operand", "expected_result"],
     [(DummyMetric(3), torch.tensor(2)), (3, torch.tensor(2)), (3, torch.tensor(2)), (torch.tensor(3), torch.tensor(2))],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_and(second_operand, expected_result):
     first_metric = DummyMetric(2)
 
@@ -92,6 +99,7 @@ def test_metrics_eq(second_operand, expected_result):
         (torch.tensor(2), torch.tensor(2)),
     ],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_floordiv(second_operand, expected_result):
     first_metric = DummyMetric(5)
 
@@ -261,6 +269,7 @@ def test_metrics_ne(second_operand, expected_result):
     ["second_operand", "expected_result"],
     [(DummyMetric([1, 0, 3]), torch.tensor([-1, -2, 3])), (torch.tensor([1, 0, 3]), torch.tensor([-1, -2, 3]))],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_or(second_operand, expected_result):
     first_metric = DummyMetric([-1, -2, 3])
 
@@ -277,10 +286,10 @@ def test_metrics_or(second_operand, expected_result):
 @pytest.mark.parametrize(
     ["second_operand", "expected_result"],
     [
-        (DummyMetric(2), torch.tensor(4)),
-        (2, torch.tensor(4)),
-        (2.0, torch.tensor(4.0)),
-        (torch.tensor(2), torch.tensor(4)),
+        pytest.param(DummyMetric(2), torch.tensor(4)),
+        pytest.param(2, torch.tensor(4)),
+        pytest.param(2.0, torch.tensor(4.0), marks=pytest.mark.skipif(**_MARK_TORCH_LOWER_1_5)),
+        pytest.param(torch.tensor(2), torch.tensor(4)),
     ],
 )
 def test_metrics_pow(second_operand, expected_result):
@@ -297,6 +306,7 @@ def test_metrics_pow(second_operand, expected_result):
     ["first_operand", "expected_result"],
     [(5, torch.tensor(2)), (5.0, torch.tensor(2.0)), (torch.tensor(5), torch.tensor(2))],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_rfloordiv(first_operand, expected_result):
     second_operand = DummyMetric(2)
 
@@ -329,8 +339,12 @@ def test_metrics_rmod(first_operand, expected_result):
 
 
 @pytest.mark.parametrize(
-    ["first_operand", "expected_result"],
-    [(DummyMetric(2), torch.tensor(4)), (2, torch.tensor(4)), (2.0, torch.tensor(4.0))],
+    "first_operand,expected_result",
+    [
+        pytest.param(DummyMetric(2), torch.tensor(4)),
+        pytest.param(2, torch.tensor(4)),
+        pytest.param(2.0, torch.tensor(4.0), marks=pytest.mark.skipif(**_MARK_TORCH_LOWER_1_5)),
+    ],
 )
 def test_metrics_rpow(first_operand, expected_result):
     second_operand = DummyMetric(2)
@@ -370,6 +384,7 @@ def test_metrics_rsub(first_operand, expected_result):
         (torch.tensor(6), torch.tensor(2.0)),
     ],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_rtruediv(first_operand, expected_result):
     second_operand = DummyMetric(3)
 
@@ -408,6 +423,7 @@ def test_metrics_sub(second_operand, expected_result):
         (torch.tensor(3), torch.tensor(2.0)),
     ],
 )
+@pytest.mark.skipif(**_MARK_TORCH_LOWER_1_4)
 def test_metrics_truediv(second_operand, expected_result):
     first_metric = DummyMetric(6)