可以使用以下代码来解决这个问题：

[assembly: System.Web.UI.WebResource("MyNamespace.MyControl.js", "text/javascript")]

[ToolboxData("<{0}:MyControl runat=server>")] public class MyControl : WebControl { protected override void OnInit(EventArgs e) { base.OnInit(e);

    if (!this.DesignMode && this.Page != null && this.Page.Header != null)
    {
        string clientScript = @"function MyControl_OnCallbackComplete(result, context) 
                                { 
                                    // Callback code here
                                }";

        ScriptManager.RegisterClientScriptBlock(this.Page, typeof(MyControl), "MyControlScript", clientScript, true);
    }
}

[WebMethod(EnableSession = true)]
[ScriptMethod(UseHttpGet = true, ResponseFormat = ResponseFormat.Json)]
public async Task GetSomeDataAsync(string param)
{
    var client = new HttpClient();
    HttpResponseMessage result = await client.GetAsync("http://example.com/api/data");
    var content = await result.Content.ReadAsStringAsync();

    return content;
}

}

这个问题通常是由于您尝试在未绑定Page的ASMX代​​码中尝试启动异步操作造成的。上面的代码示例演示了如何在OnInit事件中使用ScriptManager，以便正确地启动异步操作。