diff --git a/NEWS b/NEWS
index db1db6ac1..271d6cacb 100644
--- a/NEWS
+++ b/NEWS
@@ -242,6 +242,10 @@ New in spot 2.9.7.dev (not yet released)
   - tgba_determinize() could create parity automata using more colors
     than necessary.  (Related to issue #298)
 
+  - left->intersacting_run(right) could return a run with incorrect
+    colors (likely not corresponding to any existing transition of
+    left) if left was a weak automaton.
+
   Deprecation notices:
 
   - twa_graph::defrag_states() and digraph::defrag_states() now take
diff --git a/spot/twa/twa.cc b/spot/twa/twa.cc
index bebcbddfa..986aeb397 100644
--- a/spot/twa/twa.cc
+++ b/spot/twa/twa.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2014-2019 Laboratoire de Recherche et Developpement de
-// l'EPITA (LRDE).
+// Copyright (C) 2011, 2014-2019, 2021 Laboratoire de Recherche et
+// Developpement de l'EPITA (LRDE).
 // Copyright (C) 2003, 2004, 2005 Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
@@ -165,7 +165,14 @@ namespace spot
       {
         const_twa_graph_ptr g1 = ensure_existential_twa_graph(self);
         const_twa_graph_ptr g2 = ensure_existential_twa_graph(other);
+        // Reset g1.prop_weak() to disable the product optimization
+        // for weak automata, otherwise project(g1) would be unable to
+        // compute the correct marks.  See issue #471.  It's OK to
+        // optimize the right part if g2 is weak.
+        spot::trival g1weak = g1->prop_weak();
+        std::const_pointer_cast<twa_graph>(g1)->prop_weak(false);
         auto run = generic_accepting_run(product(g1, g2));
+        std::const_pointer_cast<twa_graph>(g1)->prop_weak(g1weak);
         if (!run)
           return nullptr;
         return run->reduce()->project(g1);
diff --git a/tests/Makefile.am b/tests/Makefile.am
index c0708f8b5..25be5e855 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -380,6 +380,7 @@ TESTS_ipython = \
 TESTS_python = \
   python/298.py \
   python/341.py \
+  python/471.py \
   python/_altscc.ipynb \
   python/_autparserr.ipynb \
   python/_aux.ipynb \
diff --git a/tests/python/471.py b/tests/python/471.py
new file mode 100644
index 000000000..6fee3a2d3
--- /dev/null
+++ b/tests/python/471.py
@@ -0,0 +1,28 @@
+# -*- mode: python; coding: utf-8 -*-
+# Copyright (C) 2021 Laboratoire de Recherche et Développement de l'Epita
+# (LRDE).
+#
+# This file is part of Spot, a model checking library.
+#
+# Spot is free software; you can redistribute it and/or modify it
+# under the terms of the GNU General Public License as published by
+# the Free Software Foundation; either version 3 of the License, or
+# (at your option) any later version.
+#
+# Spot is distributed in the hope that it will be useful, but WITHOUT
+# ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+# or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+# License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+# Test for Issue #471.
+
+import spot
+a = spot.translate('Fa')
+a = spot.to_generalized_rabin(a, False)
+r1 = a.intersecting_run(a)
+r2 = a.accepting_run()
+assert str(r1) == str(r2)
+assert a.prop_weak().is_true()