The best approach to this is to take advantage of the fact that functions are first-order objects in JavaScript. Therefore you can assign them to variables and invoke them through the variable, changing the function that the variable refers to as needed.
For example:
function firstCallback() {
// the first thing has happened
// so when the next thing happens, we want to do stuff
callback = secondCallback;
}
function secondCallback() {
// do stuff now both things have happened
}
var callback = firstCallback;
If both your pieces of code now use the variable to call the function:
callback();
then whichever one executes first will call the firstCallback, which changes the variable to point to the secondCallback, and so that will be called by whichever executes second.
However your phrasing of the question implies that this may all be unnecessary, as it sounds like you are making an Ajax request and then continuing processing. As JavaScript interpreters are single-threaded, the Ajax callback will never be executed until the main body of code that made the request has finished executing anyway, even if that is long after the response has been received.
In case that isn't your situation, I've created a working example on my site - as StackOverflow won't yet let me post links, you'll have to go to www.nickfitz.co.uk/examples/javascript/switching-functions.html manually; view the source to see the code (just before the </body> tag). It makes a request which is delayed by the server for a couple of seconds, then a request which receives an immediate response. The second request's response is handled by one function, and the first request's response is later handled by a different function, as the request that received a response first has changed the callback variable to refer to the second function.