Timer fire twice?

Hi, experts:
I started learning Swing programming by writing a demo(source code listed below) with Eclipse + JDK1.6. Please find screen shot of this demo at the end of this post.

It worked well when i press "move" button to select NEXT RadioButton. Later, i added a Swing Timer in order to select NEXT RadioButton per second (press "auto" button to start the Timer). But the next-next RadioButton was selected when i run the demo. I debugged and found the Timer Event fired twice every 1 second. What's wrong in my code?

Following is the source code:

package components;

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;
import javax.swing.Timer;

public class RadioButtonDemo extends JPanel
implements ActionListener{

/**
*
*/
private static final long serialVersionUID = 1L;

static String birdString = "Bird";
static String catString = "Cat";
static String dogString = "Dog";
static String rabbitString = "Rabbit";
static String pigString = "Pig";

JLabel buttonLabel;
JButton moveButton,autoButton,stopButton;
JRadioButton birdButton, catButton, dogButton, rabbitButton, pigButton;

Timer timer = new Timer(1000,this);

public RadioButtonDemo() {
super(new BorderLayout());

//Create the MOVE button.
moveButton = new JButton("move");
moveButton.setActionCommand("move");
//Create the AUTO button.
autoButton = new JButton("auto");
autoButton.setActionCommand("auto");
//Create the STOP button.
stopButton = new JButton("stop");
stopButton.setActionCommand("stop");
stopButton.setEnabled(false);

//Create the radio buttons.
birdButton = new JRadioButton(birdString);
birdButton.setMnemonic(KeyEvent.VK_B);
birdButton.setActionCommand(birdString);
birdButton.setSelected(true);

catButton = new JRadioButton(catString);
catButton.setMnemonic(KeyEvent.VK_C);
catButton.setActionCommand(catString);

dogButton = new JRadioButton(dogString);
dogButton.setMnemonic(KeyEvent.VK_D);
dogButton.setActionCommand(dogString);

rabbitButton = new JRadioButton(rabbitString);
rabbitButton.setMnemonic(KeyEvent.VK_R);
rabbitButton.setActionCommand(rabbitString);

pigButton = new JRadioButton(pigString);
pigButton.setMnemonic(KeyEvent.VK_P);
pigButton.setActionCommand(pigString);

//Group the radio buttons.
ButtonGroup group = new ButtonGroup();
group.add(birdButton);
group.add(catButton);
group.add(dogButton);
group.add(rabbitButton);
group.add(pigButton);

//Register a listener for the radio buttons.
birdButton.addActionListener(this);
catButton.addActionListener(this);
dogButton.addActionListener(this);
rabbitButton.addActionListener(this);
pigButton.addActionListener(this);

moveButton.addActionListener(this);
autoButton.addActionListener(this);
stopButton.addActionListener(this);

/*
//Set up the picture label.
picture = new JLabel(createImageIcon("images/"
+ birdString
+ ".gif"));

//The preferred size is hard-coded to be the width of the
//widest image and the height of the tallest image.
//A real program would compute this.
picture.setPreferredSize(new Dimension(177, 122));
*/

//Put the radio buttons in a column in a panel.
JPanel radioPanel = new JPanel(new GridLayout(0, 1));
radioPanel.add(birdButton);
radioPanel.add(catButton);
radioPanel.add(dogButton);
radioPanel.add(rabbitButton);
radioPanel.add(pigButton);

add(radioPanel, BorderLayout.LINE_START);
add(moveButton,BorderLayout.NORTH);
add(autoButton,BorderLayout.CENTER);
add(stopButton,BorderLayout.EAST);
setBorder(BorderFactory.createEmptyBorder(20,20,20 ,20));
}

/** Listens to the radio buttons. */
public void actionPerformed(ActionEvent e) {
if ("move".equals(e.getActionCommand()) || "timer".equals(e.getActionCommand())) {
if(birdButton.isSelected()){
catButton.setSelected(true);
}
else if(catButton.isSelected()){
dogButton.setSelected(true);
}
else if(dogButton.isSelected()){
rabbitButton.setSelected(true);
}
else if(rabbitButton.isSelected()){
pigButton.setSelected(true);
}
else if(pigButton.isSelected()){
birdButton.setSelected(true);
}
}

else if("auto".equals(e.getActionCommand())){

timer.addActionListener(this);
timer.setActionCommand("timer");
timer.setInitialDelay(1000);
timer.start();
stopButton.setEnabled(true);
}
else if("stop".equals(e.getActionCommand())){
timer.stop();
stopButton.setEnabled(false);
}

}

/** Returns an ImageIcon, or null if the path was invalid. */
/*protected static ImageIcon createImageIcon(String path) {
java.net.URL imgURL = RadioButtonDemo.class.getResource(path);
if (imgURL != null) {
return new ImageIcon(imgURL);
} else {
System.err.println("Couldn't find file: " + path);
return null;
}
}*/

/**
* Create the GUI and show it. For thread safety,
* this method should be invoked from the
* event-dispatching thread.
*/
private static void createAndShowGUI() {
//Create and set up the window.
JFrame frame = new JFrame("RadioButtonDemo");
frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOS E);

//Create and set up the content pane.
JComponent newContentPane = new RadioButtonDemo();
newContentPane.setOpaque(true); //content panes must be opaque
frame.setContentPane(newContentPane);

//Display the window.
frame.pack();
frame.setVisible(true);
}

public static void main(String[] args) {
//Schedule a job for the event-dispatching thread:
//creating and showing this application's GUI.
javax.swing.SwingUtilities.invokeLater(new Runnable() {
public void run() {
createAndShowGUI();
}
});
}

}

Anybody help?
Thanks a lot.