How to use several wp_ajax_ functions for different queries?

I was able to get multiple wp_ajax_ functions to declare callback functions like this:

add_action( 'init', 'my_ajax_init' );
function my_ajax_init() {
    add_action('wp_ajax_nopriv_wpa56343_search', 'first_search');
    add_action('wp_ajax_wpa56343_search', 'first_search');
}

add_action( 'init', 'my_ajax_no_geo_init' );
function my_ajax_no_geo_init() {
    add_action('wp_ajax_nopriv_nogeo_results', 'second_search');
    add_action('wp_ajax_nogeo_results', 'second_search');
}