I am using jsf2.0 with primefaces.My application was working fine with all browsers includes IE8... but when i run my application in IE9 my internal stylesheet not even take
I checked your website chennaivolunteers.org and I noticed that FacesServlet is been mapped on an URL pattern of /faces/* instead of *.xhtml. As you're using only relative and resource references, they will (unnecessarily) go through the FacesServlet as well.
IE9 sends for CSS files a Accept-Header of text/css while other browsers sends a Accept-Header of text/css;*/*. The FacesServlet itself is not supposed to respond on text/css requests.
There are basically 2 ways to fix this:
Get rid of the /faces/* mapping and replace it by *.xhtml.
Faces Servlet
*.xhtml
Use domain-relative URLs in and (and ) references so that they never go through the /faces path.
Or use the tag, or use and with a name instead.
Your site has by the way quite some 404's on several resources. Fix that as well. Check the "Net", "Network" section of the browser's builtin web developer toolset (press F12 in IE9/Chrome/Firebug).