Session Problem

Hi all,

i developed one sample site www.MySite.com.
It contains one login page, customer entry page and Send Message.

i opened this site in IE (my pc).

In login page i entered username(X) and password. After authenticate i transfer to customer entry page.

i maintained UserName in Session.(Session["UserName"] = x;)

Again i opened www.MySite.Com in browser(Same Pc) this time some 'y' person login into site.
 i am transfer to SendMessage Page.(Session["UserName"] = y;

Here my problem is once i openend two instances for my site in same pc with different users login.
My Session["UserName"] is name is changing user 'X' to 'Y'.

Sessions are overriding.But sessions are have unique id's.
please tell me how to resolve this issue.

Regards,
Jeevan.