I can call the webservie directly to the browser with the following URL and it returns be all what I want :
http://localhost:64438/MySearchAutoComplete.asmx/GetCompletionList
When I add it to an autocompleteexetender into the Default.aspx page like that :
<cc1:AutoCompleteExtender ID="AutoCompleteExtender1" 
                  TargetControlID="TextBox1" 
                  runat="server" 
                  ServiceMethod="GetCompletionList" 
                  ServicePath="http://localhost:64438/MySearchAutoComplete.asmx" 
                  CompletionSetCount="12"
                  MinimumPrefixLength="1" />
The page load, I have a textbox but I have an error 500 every time I add a keystroke in the textbox. I see the error in the FireFox FireBug.
http://localhost:62702/   --->This is the webpage that load fine 
 --> This is the error
 --> This is the error
Any idea? I have noticed that I need to attach the process to debug the webservice, I might do something wrong with it too?
Edit (Event Viewer)
If I go to the Event Viewer of my machine. I can see :
Exception information: 
    Exception type: InvalidOperationException 
    Exception message: Request format is unrecognized for URL unexpectedly ending in '/GetCompletionList'. 
    Thread information: 
    Thread ID: 8 
    Thread account name: MTL\daok 
    Is impersonating: False 
    Stack trace:    at     System.Web.Services.Protocols.WebServiceHandlerFactory.CoreGetHandler(Type type, HttpContext context, HttpRequest request, HttpResponse response)
   at System.Web.Services.Protocols.WebServiceHandlerFactory.GetHandler(HttpContext context, String verb, String url, String filePath)
   at System.Web.HttpApplication.MapHttpHandler(HttpContext context, String requestType, VirtualPath path, String pathTranslated, Boolean useAppConfig)
   at System.Web.HttpApplication.MapHandlerExecutionStep.System.Web.HttpApplication.IExecutionStep.Execute()
   at System.Web.HttpApplication.ExecuteStep(IExecutionStep step, Boolean& completedSynchronously)
I also have to start the webservice project first, than I stop it and start the webproject to be able to have both. The webservice still works (I can fire it directly http://localhost:64438/MySearchAutoComplete.asmx?op=GetCompletionList) but on the webpage I still have that Error 500.
Edit 2 (Web.config)
Adding to the webservice project web.config:
  <webServices>
    <protocols>
      <add   name="HttpGet"/>
      <add   name="HttpPost"/>
    </protocols>
  </webServices>
Have not solve the problem.
Edit 3 (Direct call)
Calling in the Page_Load() the same method from the WebService work very well:
     string[] stuffs;
     stuffs = proxy.GetCompletionList("1", 10);
     MyList.DataSource = stuffs;
     MyList.DataBind();
But it's not working with the AutoCompleteExtender...