diff --git a/.github/workflows/ci_msw_cross.yml b/.github/workflows/ci_msw_cross.yml
index 26c8bf9d17..4831f1a1ef 100644
--- a/.github/workflows/ci_msw_cross.yml
+++ b/.github/workflows/ci_msw_cross.yml
@@ -197,7 +197,29 @@ jobs:
 
           httpbin_launch
 
-          $wxTEST_RUNNER ./test || rc=$?
+          # Some tests are currently failing under Wine while they pass under
+          # native MSW, just skip running them until they can be dealt with.
+
+          # As soon as we specify the tests to exclude explicitly, we also need
+          # to exclude the tests that are not run by default, so start with this.
+          excluded_tests=('~[.]')
+
+          # Only TestSetTimes fails, but only the full test can be excluded.
+          excluded_tests+=('~FileNameTestCase')
+
+          # Only FileError fails, but the whole test has to be excluded.
+          excluded_tests+=('~FileFunctionsTestCase')
+
+          # Sporadic failures due to extra events.
+          excluded_tests+=('~wxFileSystemWatcher::EventCreate')
+
+          # The test fails (even with wxTEST_RUNNER-related changes) and hangs.
+          excluded_tests+=('~ExecTestCase')
+
+          # Wine WinHTTP implementations seems buggy, there are many errors.
+          excluded_tests+=('~[webrequest]')
+
+          $wxTEST_RUNNER ./test "${excluded_tests[@]}" || rc=$?
 
           if [ -n "$rc" ]; then
             httpbin_show_log
@@ -207,4 +229,28 @@ jobs:
       - name: Run GUI tests
         working-directory: tests
         run: |
-          $wxTEST_RUNNER ./test_gui
+          # Same as for the non-GUI test above, except many more GUI tests fail
+          # under Wine.
+          excluded_gui_tests=('~[.]')
+
+          excluded_gui_tests+=('~BitmapComboBoxTestCase') # TextChangeEvents
+          excluded_gui_tests+=('~ClippingBoxTestCase*')
+          excluded_gui_tests+=('~ComboBoxTestCase') # TextChangeEvents
+          excluded_gui_tests+=('~DatePickerCtrlTestCase') # Range
+          excluded_gui_tests+=('~wxDC::GetTextExtent')
+          excluded_gui_tests+=('~ExecTestCase')
+          excluded_gui_tests+=('~wxFont::GetSet')
+          excluded_gui_tests+=('~GraphicsPathTestCaseGDIPlus')
+          excluded_gui_tests+=('~ImageList*')
+          excluded_gui_tests+=('~RadioButton::Focus')
+          excluded_gui_tests+=('~SettingsTestCase') # GetFont fails
+          excluded_gui_tests+=('~SliderTestCase')   # Thumb
+          excluded_gui_tests+=('~TransformMatrixTestCase*')
+          excluded_gui_tests+=('~TreeCtrlTestCase') # LabelEdit
+          excluded_gui_tests+=('~TextCtrlTestCase') # many sub-tests
+          excluded_gui_tests+=('~wxTextCtrl::InitialCanUndo')
+          excluded_gui_tests+=('~[wxWebView]')
+          excluded_gui_tests+=('~Window::PositioningBeyondShortLimit')
+          excluded_gui_tests+=('~XRC::LoadURL')
+
+          $wxTEST_RUNNER ./test_gui "${excluded_gui_tests[@]}"