The default async for Ajax in jQuery is true(asynchronous request). If you want to execute one Ajax before executing another Ajax, you need to put async=false.

The code is as follows:

function TestAjax()
{
 var UserName = $("#txtUserName").val();
 $.ajax({
  url:"AjaxCheckUserName.htm",
  async:false,
  success:function(data){
   alert(data);
  }
 });
 alert('Test');
 $.ajax({
  url:"AjaxHandler.ashx",
  async:false,
  data:"UserName=" + UserName,
  success:function(data){
   $("#divAjax").html(data);
  },
  error:function(msg){
   alert(msg.responseText);
  }
 });
}

Next, take a look at the order in which jquery $.ajax executes each event

The execution sequence is as follows:

1.ajaxStart(Global Events)

2.beforeSend

3.ajaxSend(Global events)

4.success

5.ajaxSuccess(Global Events)

6.error

7.ajaxError (Global Events)

8.complete

9.ajaxComplete(Global events)

10.ajaxStop(Global events)