ASP.NET de async işlem yapabilmek için JQueryden faydalanmanız gerekiyor.
Bunu 2 yöntem ile yapmak mümkün

1. ScriptManager
2. JQuery methodları ile

2. methoda daha dogal geldiginden işlemlerimizi onunla gerçekleştiricez.

a) İlk olarak .cs tarafında methodumuzu yazalım :

[System.Web.Services.WebMethod]
        public static string Kaydet(string a,string b)
        {
            string result = "OK : " + a + " - ";
            return result;
        } 

b) Şimdi JQuery kütüphaneleri eklediginizi düşünerek hemen HTML kontrolün çağıracagı JS methoda oluşturalım :

     function Kaydetsene(a,b) {
    $.ajax({
        type: "POST",
        url: "sevkiyatci.aspx/Kaydet",
        data: "{a:'aaaa',b:'bb'}",
        contentType: "application/json;",
        dataType: "json",
        success: function(response) { alert("OK : "+ response.d);},
        failure: function(response) { alert("HATA : "+ response.d);}
    });
}

c) Son alarakda methodu control üzerindeki bi event ile çagırıyoruz

 OnClick='<%# Eval("Fat_No","Kaydetsene(\"{0}\",\"2\");") %>'  

 OnClick='<%# "Kaydetsene(\"" + Eval("Fat_No") + "\",\"2\");" %>' 

//-----digerleri------

var k = $('[id$=lbl_kim]').attr('title');
var params = "{'Kimden':'"+k+"'}";

$('#okun').text('0');

setTimeout("GetMSJsayisi();", 10000);

// digerleri iki - eger farklı ise

  <system.webServer>

    <validation validateIntegratedModeConfiguration="false"/>

    <modules>

      <remove name="ScriptModule"/>

      <add name="ScriptModule" preCondition="managedHandler" type="System.Web.Handlers.ScriptModule, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>

    </modules>

    <handlers>

      <remove name="WebServiceHandlerFactory-Integrated"/>

      <remove name="ScriptHandlerFactory"/>

      <remove name="ScriptHandlerFactoryAppServices"/>

      <remove name="ScriptResource"/>

      <add name="ScriptHandlerFactory" verb="*" path="*.asmx" preCondition="integratedMode" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>

      <add name="ScriptHandlerFactoryAppServices" verb="*" path="*_AppService.axd" preCondition="integratedMode" type="System.Web.Script.Services.ScriptHandlerFactory, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>

      <add name="ScriptResource" preCondition="integratedMode" verb="GET,HEAD" path="ScriptResource.axd" type="System.Web.Handlers.ScriptResourceHandler, System.Web.Extensions, Version=3.5.0.0, Culture=neutral, PublicKeyToken=31BF3856AD364E35"/>

    </handlers>

  </system.webServer> 

//----------------- dropdownlist

JavaScript ile:

var e = document.getElementById("elementId");
var value = e.options[e.selectedIndex].value;
var text = e.options[e.selectedIndex].text;

jQuery ile:

$("#elementId :selected").text(); // The text content of the selected option
$("#elementId").val(); // The value of the selected option