Hi!.
i think you need updatepanel for this
first you need AJAX extensions VS2010 has this toolbox
first thing to do drag and drop script manager to you page or to your master page
so ajax script can be used
*note
script manager need just for one page
but if you have masterpage you can put it there so you would not put it again.
then drag and drop update panel to your page
then after that under update panel put ContentTemplate
then put your dropdownlist inside contenttemplate
the code will look like this
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
<ContentTemplate>
<asp:DropDownList ID="DDL1st" runat="server">
</asp:DropDownList>
<asp:DropDownList ID="DDL2nd" runat="server" AutoPostBack="True">
</asp:DropDownList>
</ContentTemplate>
Look at 2nd DDL the autopostback=true so that any event that fired by 2nd dll will be executed
remember all of this is inside the updatepanel so all post back will be handle without refreshing your page.
i hope this is the answer to your question