The obvious answer is -

jcombobox.addMouseListener(
  new MouseAdapter() {
     public void mouseClicked(MouseEvent me) {
        if (me.getClickCount() == 2) {
            // double click.
        }
     }
  }
);

Is your JComboBox editable ? If so the
JComboBox editor may be kicking in after
first click and intercepting your second click.