Quindi ad esempio in questo modo ?

codice:
class NuovoAnnuncio extends JFrame  {

	public NuovoAnnuncio() { super("Inserisci Annuncio");
        initialize();
    }


 void initialize() {
    	
        setSize(665,620);
        setResizable(false); 
        setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);     
        addWindowListener(new close());

class close implements WindowListener {
	      public void windowActivated(WindowEvent w) {
	      }

	      
		public void windowClosed(WindowEvent w) { 	  
	      	
	      
	      }

	      public void windowClosing(WindowEvent w) {
	    	  final JFrame uscire = new JFrame();  
	    	  
		      	uscire.setDefaultCloseOperation(JFrame.DO_NOTHING_ON_CLOSE);	  
		      	uscire.setLayout(new FlowLayout());
		      	uscire.setSize(260,120);
		      	uscire.setResizable(false);
		      	JPanel info = new JPanel();
		          info.setLayout(new GridLayout(0,1));
		      	
		      	JTextField salvataggio;     
		          salvataggio = new JTextField("Uscire dal programma?",12);
		          salvataggio.setEditable(false);
		          salvataggio.setFont(labelfont);
		          JPanel salvaesci = new JPanel();
		          salvaesci.setLayout(new GridLayout(0,2));
		          
		          JButton no = new JButton("No");        
		          no.setFont(buttonfont);
		          JButton si = new JButton("Si");        
		          si.setFont(buttonfont);
		          info.add(salvataggio);                    		                
		          salvaesci.add(si); 
		          salvaesci.add(no);
		          
		          uscire.add(info);
		          uscire.add(salvaesci);
		          si.addActionListener(new ActionListener() {
		              public void actionPerformed(ActionEvent event) {              
		              	System.exit(0);
		              	
		                                 
		              }

		  			
		              
		          });
		          no.addActionListener(new ActionListener() {
		              @SuppressWarnings("deprecation")
					public void actionPerformed(ActionEvent event) {           
		              	
		              	uscire.hide();	        
		                                 
		              }
		              
		          });
		          
	      }

	      public void windowDeactivated(WindowEvent w) {
	      }

	      public void windowDeiconified(WindowEvent w) {
	      }

	      public void windowIconified(WindowEvent w) {
	      }

	      public void windowOpened(WindowEvent w) {
	      }
	    };
}
    	
		 	
			
	            public void run() {
	                new NuovoAnnuncio().setVisible(true);
	                
	            }
	        
			
		}
facendo così però non succede nulla quando clicco sulla "X"