diff --git a/poetry/core/packages/__init__.py b/poetry/core/packages/__init__.py
index 16854c530..7c1c05f61 100644
--- a/poetry/core/packages/__init__.py
+++ b/poetry/core/packages/__init__.py
@@ -165,7 +165,7 @@ def dependency_from_pep_508(
             ands = []
             for op, version in or_:
                 # Expand python version
-                if op == "==":
+                if op == "==" and "*" not in version:
                     version = "~" + version
                     op = ""
                 elif op == "!=":
diff --git a/tests/packages/test_main.py b/tests/packages/test_main.py
index 34cd954ef..3df41fefd 100644
--- a/tests/packages/test_main.py
+++ b/tests/packages/test_main.py
@@ -236,3 +236,21 @@ def test_dependency_from_pep_508_with_python_full_version():
         'python_version >= "2.7" and python_version < "2.8" '
         'or python_full_version >= "3.4" and python_full_version < "3.5.4"'
     )
+
+
+def test_dependency_from_pep_508_with_python_full_version_pep440_compatible_release_astrix():
+    name = 'pathlib2 ; python_version == "3.4.*" or python_version < "3"'
+    dep = dependency_from_pep_508(name)
+
+    assert dep.name == "pathlib2"
+    assert str(dep.constraint) == "*"
+    assert dep.python_versions == "==3.4.* || <3"
+
+
+def test_dependency_from_pep_508_with_python_full_version_pep440_compatible_release_tilde():
+    name = 'pathlib2 ; python_version ~= "3.4" or python_version < "3"'
+    dep = dependency_from_pep_508(name)
+
+    assert dep.name == "pathlib2"
+    assert str(dep.constraint) == "*"
+    assert dep.python_versions == "~=3.4 || <3"
diff --git a/tests/semver/test_parse_constraint.py b/tests/semver/test_parse_constraint.py
index b628f94a5..f70c5741e 100644
--- a/tests/semver/test_parse_constraint.py
+++ b/tests/semver/test_parse_constraint.py
@@ -10,6 +10,10 @@
     "constraint,version",
     [
         ("~=3.8", VersionRange(min=Version(3, 8), max=Version(4, 0), include_min=True)),
+        (
+            "== 3.8.*",
+            VersionRange(min=Version(3, 8), max=Version(3, 9, 0), include_min=True),
+        ),
         (
             "~= 3.8",
             VersionRange(min=Version(3, 8), max=Version(4, 0), include_min=True),