Index: core/src/main/java/quickfix/Session.java
===================================================================
--- core/src/main/java/quickfix/Session.java	(revision 1114)
+++ core/src/main/java/quickfix/Session.java	(working copy)
@@ -1289,7 +1289,10 @@
 
         state.setLogoutReceived(true);
 
-        state.incrNextTargetMsgSeqNum();
+        final int logoutMsgSeqNum = logout.getHeader().getInt(MsgSeqNum.FIELD);
+        if (!isTargetTooHigh(logoutMsgSeqNum)) {
+            state.incrNextTargetMsgSeqNum();
+        }
         if (resetOnLogout) {
             resetState();
         }
Index: core/src/test/java/quickfix/SessionTest.java
===================================================================
--- core/src/test/java/quickfix/SessionTest.java	(revision 1114)
+++ core/src/test/java/quickfix/SessionTest.java	(working copy)
@@ -345,6 +345,41 @@
 
     }
 
+    // QFJ-750
+    @Test
+    public void testLogoutMsgSeqNumTooHigh() throws Exception {
+
+        final Application application = new UnitTestApplication();
+        final Session session = setUpSession(application, false, new UnitTestResponder());
+        final SessionState state = getSessionState(session);
+
+        assertEquals(1, state.getNextSenderMsgSeqNum());
+        assertEquals(1, state.getNextTargetMsgSeqNum());
+
+        logonTo(session);
+
+        assertEquals(2, state.getNextSenderMsgSeqNum());
+        assertEquals(2, state.getNextTargetMsgSeqNum());
+
+        final TestRequest testRequest = (TestRequest) createAdminMessage(2);
+        session.next(testRequest);
+
+        assertEquals(3, state.getNextSenderMsgSeqNum());
+        assertEquals(3, state.getNextTargetMsgSeqNum());
+
+        logoutFrom(session, 100);
+        assertFalse("Session should be disconnected", session.isLoggedOn());
+
+        // make sure that the target seq num has not been incremented
+        assertEquals(4, state.getNextSenderMsgSeqNum());
+        assertEquals(3, state.getNextTargetMsgSeqNum());
+        logonTo(session, 3);
+        assertEquals(5, state.getNextSenderMsgSeqNum());
+        assertEquals(4, state.getNextTargetMsgSeqNum());
+        assertTrue("Session should be connected", session.isLoggedOn());
+
+    }
+
     /**
      * QFJ-357
      * Until QF/J 1.5.1 the behaviour was observed that a Logout message was always sent as first message.
@@ -1114,6 +1149,14 @@
         session.next(receivedLogon);
     }
 
+    private void logoutFrom(Session session, int sequence) throws FieldNotFound, RejectLogon,
+            IncorrectDataFormat, IncorrectTagValue, UnsupportedMessageType, IOException,
+            InvalidMessage {
+        final Logout receivedLogout = new Logout();
+        setUpHeader(session.getSessionID(), receivedLogout, true, sequence);
+        session.next(receivedLogout);
+    }
+
     private void setUpHeader(SessionID sessionID, Message message, boolean reversed, int sequence) {
         message.getHeader().setString(TargetCompID.FIELD,
                 reversed ? sessionID.getSenderCompID() : sessionID.getTargetCompID());