Using AJAX for dynamic settings pages

I have a settings page like ...

add_options_page ( 'XXX', 'XXX', 'manage_options', 'xxx_plugin', 'xxx_options_page' );

function xxx_options_page() { ?>
<div class="wrap">
    <h2><?php _e('XXX Settings', 'xxx'); ?> </h2>

    <form action="options.php" method="post">
        <?php settings_fields('xxx_plugin_options'); ?>
        <?php $options = get_option('xxx_options'); ?>
        <?php $t = xxx_get...; ?>
        <table class="form-table">

        <select name='xxx_options[foobar]'>
            <?php foreach($t as $key => $value) { ?>
                <option value='<?php echo $key ?>' <?php selected($key, $options['xxx']); ?>><?php echo $value ?></option>
            <?php } ?>  
        </select>        
        // ... more elements, submit-button, ...       
  </form>
<?php } ?>

I need to add another select-element, thoose values depends on the selection of the first select-element.

For example: First select-element: Select Country -> Second select element: Select states of selected country -> Third select element: Select cities of selected state.

I think, I cannot do this without Ajax, but I did not found some matching example or an tutorial how to do that with WP and Ajax. Any ideas? Any examples? TIA!