diff --git a/src/tests/stutter-tgba.test b/src/tests/stutter-tgba.test
index dd3f69d03..63430890c 100755
--- a/src/tests/stutter-tgba.test
+++ b/src/tests/stutter-tgba.test
@@ -70,6 +70,8 @@ State: 2
 --END--
 EOF
 
+diff output expected
+
 run 0 $ltl2tgba -H 'F(a & X(!a & b))' > input
 grep stutter-invariant input && exit 1
 run 0 $ltl2tgba --check=stutter 'F(a & X(!a & b))' > input.2
@@ -77,4 +79,9 @@ grep stutter-invariant input.2
 run 0 $autfilt --check=stutter input > input.2
 grep stutter-invariant input.2
 
-diff output expected
+run 0 $ltl2tgba -H 'F(a & X(a & b))' > input
+grep stutter-invariant input && exit 1
+run 0 $ltl2tgba --check=stutter 'F(a & X(a & b))' > input.2
+grep stutter-sensitive input.2
+run 0 $autfilt --check=stutter input > input.2
+grep stutter-sensitive input.2
diff --git a/src/twa/twa.hh b/src/twa/twa.hh
index 54d752fd6..bb50212ec 100644
--- a/src/twa/twa.hh
+++ b/src/twa/twa.hh
@@ -715,7 +715,8 @@ namespace spot
       bool state_based_acc:1;	// State-based acceptance.
       bool inherently_weak:1;	// Weak automaton.
       bool deterministic:1;	// Deterministic automaton.
-      bool stutter_inv:1; 	// Stutter invariant
+      bool stutter_invariant:1;	// Stutter invariant language.
+      bool stutter_sensitive:1;	// Stutter sensitive language.
     };
     union
     {
@@ -798,12 +799,22 @@ namespace spot
 
     bool is_stutter_invariant() const
     {
-      return is.stutter_inv;
+      return is.stutter_invariant;
+    }
+
+    bool is_stutter_sensitive() const
+    {
+      return is.stutter_sensitive;
     }
 
     void prop_stutter_invariant(bool val = true)
     {
-      is.stutter_inv = val;
+      is.stutter_invariant = val;
+    }
+
+    void prop_stutter_sensitive(bool val = true)
+    {
+      is.stutter_sensitive = val;
     }
 
     struct prop_set
@@ -830,7 +841,10 @@ namespace spot
       if (p.deterministic)
 	prop_deterministic(other->is_deterministic());
       if (p.stutter_inv)
-	prop_stutter_invariant(other->is_stutter_invariant());
+	{
+	  prop_stutter_invariant(other->is_stutter_invariant());
+	  prop_stutter_sensitive(other->is_stutter_sensitive());
+	}
     }
 
     void prop_keep(prop_set p)
@@ -841,6 +855,11 @@ namespace spot
 	prop_inherently_weak(false);
       if (!p.deterministic)
 	prop_deterministic(false);
+      if (!p.stutter_inv)
+	{
+	  prop_stutter_invariant(false);
+	  prop_stutter_sensitive(false);
+	}
     }
 
   };
diff --git a/src/twaalgos/hoa.cc b/src/twaalgos/hoa.cc
index 1c9c11dd7..7068d0804 100644
--- a/src/twaalgos/hoa.cc
+++ b/src/twaalgos/hoa.cc
@@ -327,8 +327,11 @@ namespace spot
       prop(" complete");
     if (md.is_deterministic)
       prop(" deterministic");
+    assert(!(aut->is_stutter_invariant() && aut->is_stutter_sensitive()));
     if (aut->is_stutter_invariant())
       prop(" stutter-invariant");
+    if (aut->is_stutter_sensitive())
+      prop(" stutter-sensitive");
     if (aut->is_inherently_weak())
       prop(" inherently-weak");
     os << nl;
diff --git a/src/twaalgos/stutter.cc b/src/twaalgos/stutter.cc
index 098108538..985f55196 100644
--- a/src/twaalgos/stutter.cc
+++ b/src/twaalgos/stutter.cc
@@ -667,8 +667,8 @@ namespace spot
 
     is_stut = is_stutter_invariant(make_twa_graph(aut, twa::prop_set::all()),
 				   std::move(neg), get_all_ap(aut));
-    if (is_stut)
-      aut->prop_stutter_invariant(is_stut);
+    aut->prop_stutter_invariant(is_stut);
+    aut->prop_stutter_sensitive(!is_stut);
     return is_stut;
   }
 }