JTextArea textarea = new JTextArea();
    final UndoManager undo = new UndoManager();
    Document doc = textarea.getDocument();
    
    doc.addUndoableEditListener(new UndoableEditListener() {
        public void undoableEditHappened(UndoableEditEvent evt) {
            undo.addEdit(evt.getEdit());
        }
    });
    
    textarea.getActionMap().put("Undo",
        new AbstractAction("Undo") {
            public void actionPerformed(ActionEvent evt) {
                try {
                    if (undo.canUndo()) {
                        undo.undo();
                    }
                } catch (CannotUndoException e) {
                }
            }
        });
    textarea.getInputMap().put(KeyStroke.getKeyStroke("control Z"), "Undo");
    
    textarea.getActionMap().put("Redo",
        new AbstractAction("Redo") {
            public void actionPerformed(ActionEvent evt) {
                try {
                    if (undo.canRedo()) {
                        undo.redo();
                    }
                } catch (CannotRedoException e) {
                }
            }
        });
    textarea.getInputMap().put(KeyStroke.getKeyStroke("control Y"), "Redo");