Hello ,
You can use the update panel control like below ..
<asp:scriptmanager id="ScriptManager1" runat="server" xmlns:asp="#unknown">
</asp:scriptmanager>
<asp:updatepanel id="UpdatePanel1" runat="server" xmlns:asp="#unknown">
<contenttemplate>
<asp:dropdownlist runat="server">
</asp:dropdownlist>
<asp:dropdownlist runat="server">
</asp:dropdownlist>
</contenttemplate>
</asp:updatepanel>
and if you want use javascript then use
<asp:dropdownlist runat="server" autopostback="false" onselectedindexchanged="" xmlns:asp="#unknown">
</asp:dropdownlist>