YOu can use Javascript
in aspx
<asp:dropdownlist onchange="onchange()" id="Dropdownlist1" runat="server" xmlns:asp="#unknown">
</asp:dropdownlist>
<asp:dropdownlist id="Dropdownlist2" runat="server" xmlns:asp="#unknown">
</asp:dropdownlist>
this js should write down after your above html
function onchange()
{
var dl1=document.getElementById("Dropdownlist1");
var dl2=document.getElementById("Dropdownlist2");
if(dl1.options[dl1.selectedIndex].text=="your text")
dl2.style.display="none";
if(dl1.value=="your value")
dl2.style.display="none";
}