Would say the callback for the new Ajax.Request have the secondary Ajax call in it. Otherwise they'll both run at the same time. Not sure why you'd need two Ajax calls for this though, can you not send back a JSON object with both the selectbox and the secondary selectbox from the server side?
<script type="text/javascript">
new Ajax.Request(
'/ajax.php',
method:'post',
parameters:{variable:'blah blah blah'},
onSuccess:function(transport) {
// Update the select box.
new Ajax.Request(
'/ajax.php',
method:'post',
parameters:{variable:'blah blah blah'},
onSuccess:function(transport) {
// Second call, this time the selectbox is updated.
}
);
}
);
</script>