diff --git a/src/poetry/core/version/markers.py b/src/poetry/core/version/markers.py
index 00caa879f..c3b64fe10 100644
--- a/src/poetry/core/version/markers.py
+++ b/src/poetry/core/version/markers.py
@@ -397,39 +397,51 @@ def __init__(self, *markers: MarkerTypes) -> None:
 
     @classmethod
     def of(cls, *markers: MarkerTypes) -> MarkerTypes:
-        new_markers = []
-        markers = _flatten_markers(markers, MultiMarker)
+        new_markers = _flatten_markers(markers, MultiMarker)
+        markers = []
 
-        for marker in markers:
-            if marker in new_markers:
-                continue
+        while markers != new_markers:
+            markers = new_markers
+            new_markers = []
+            for marker in markers:
+                if marker in new_markers:
+                    continue
 
-            if marker.is_any():
-                continue
+                if marker.is_any():
+                    continue
 
-            if isinstance(marker, SingleMarker):
-                intersected = False
-                for i, mark in enumerate(new_markers):
-                    if (
-                        not isinstance(mark, SingleMarker)
-                        or isinstance(mark, SingleMarker)
-                        and mark.name != marker.name
-                    ):
+                if isinstance(marker, SingleMarker):
+                    intersected = False
+                    for i, mark in enumerate(new_markers):
+                        if isinstance(mark, SingleMarker) and mark.name == marker.name:
+                            intersection = mark.constraint.intersect(marker.constraint)
+                            if intersection == mark.constraint:
+                                intersected = True
+                            elif intersection == marker.constraint:
+                                new_markers[i] = marker
+                                intersected = True
+                            elif intersection.is_empty():
+                                return EmptyMarker()
+                        elif isinstance(mark, MarkerUnion):
+                            intersection = mark.intersect(marker)
+                            if isinstance(intersection, SingleMarker):
+                                new_markers[i] = intersection
+                            elif intersection.is_empty():
+                                return EmptyMarker()
+                    if intersected:
                         continue
 
-                    intersection = mark.constraint.intersect(marker.constraint)
-                    if intersection == mark.constraint:
-                        intersected = True
-                    elif intersection == marker.constraint:
-                        new_markers[i] = marker
-                        intersected = True
-                    elif intersection.is_empty():
-                        return EmptyMarker()
+                elif isinstance(marker, MarkerUnion):
+                    for mark in new_markers:
+                        if isinstance(mark, SingleMarker):
+                            intersection = marker.intersect(mark)
+                            if isinstance(intersection, SingleMarker):
+                                marker = intersection
+                                break
+                            elif intersection.is_empty():
+                                return EmptyMarker()
 
-                if intersected:
-                    continue
-
-            new_markers.append(marker)
+                new_markers.append(marker)
 
         if any(m.is_empty() for m in new_markers) or not new_markers:
             return EmptyMarker()
@@ -576,7 +588,7 @@ def of(cls, *markers: BaseMarker) -> MarkerTypes:
             return AnyMarker()
 
         if not markers:
-            return AnyMarker()
+            return EmptyMarker()
 
         if len(markers) == 1:
             return markers[0]
diff --git a/tests/version/test_markers.py b/tests/version/test_markers.py
index a317205aa..ee2a3c62d 100644
--- a/tests/version/test_markers.py
+++ b/tests/version/test_markers.py
@@ -124,6 +124,24 @@ def test_single_marker_intersect_with_multi_compacts_constraint():
     )
 
 
+def test_single_marker_intersect_with_union_leads_to_single_marker():
+    m = parse_marker('python_version >= "3.6"')
+
+    intersection = m.intersect(
+        parse_marker('python_version < "3.6" or python_version >= "3.7"')
+    )
+    assert str(intersection) == 'python_version >= "3.7"'
+
+
+def test_single_marker_intersect_with_union_leads_to_empty():
+    m = parse_marker('python_version == "3.7"')
+
+    intersection = m.intersect(
+        parse_marker('python_version < "3.7" or python_version >= "3.8"')
+    )
+    assert intersection.is_empty()
+
+
 def test_single_marker_not_in_python_intersection():
     m = parse_marker('python_version not in "2.7, 3.0, 3.1"')
 
@@ -259,6 +277,36 @@ def test_multi_marker_intersect_multi_with_overlapping_constraints():
     )
 
 
+def test_multi_marker_intersect_with_union_drops_union():
+    m = parse_marker('python_version >= "3" and python_version < "4"')
+    m2 = parse_marker('python_version < "2" or python_version >= "3"')
+    assert str(m.intersect(m2)) == str(m)
+    assert str(m2.intersect(m)) == str(m)
+
+
+def test_multi_marker_intersect_with_multi_union_leads_to_empty_in_one_step():
+    # empty marker in one step
+    # py == 2 and (py < 2 or py >= 3) -> empty
+    m = parse_marker('sys_platform == "darwin" and python_version == "2"')
+    m2 = parse_marker(
+        'sys_platform == "darwin" and (python_version < "2" or python_version >= "3")'
+    )
+    assert m.intersect(m2).is_empty()
+    assert m2.intersect(m).is_empty()
+
+
+def test_multi_marker_intersect_with_multi_union_leads_to_empty_in_two_steps():
+    # empty marker in two steps
+    # py >= 2 and (py < 2 or py >= 3) -> py >= 3
+    # py < 3 and py >= 3 -> empty
+    m = parse_marker('python_version >= "2" and python_version < "3"')
+    m2 = parse_marker(
+        'sys_platform == "darwin" and (python_version < "2" or python_version >= "3")'
+    )
+    assert m.intersect(m2).is_empty()
+    assert m2.intersect(m).is_empty()
+
+
 def test_multi_marker_union_multi():
     m = parse_marker('sys_platform == "darwin" and implementation_name == "cpython"')