You need to update your Xandros Linux distribution to a newer version if you want to use current Firefox versions.

You can look at http://en.wikipedia.org/wiki/Ubuntu_Netbook_Remix

Depending upon which EeePC you have, the Celeron 900MHz version or a newer Atom 1.6 GHZ version and how large your "hard drive" is, there's a few different Linux distros to look at.

Ubuntu Netbook Edition - http://www.ubuntu.com/netbook - is a good choice for the Atom processor and an actual hard drive. But if you have one of the 7" or 9" models with the Celeron 900 MHz processor and a 2Gb or 4Gb SSD, there are other distros to look at. Those distros have the drivers used by those older ASUS EeePC models, without burdening the limited drive space with other drivers and a lot of software that you mat not need. Overall, they have a smaller installation footprint and are faster, while using less from the battery.
http://www.leeenux-linux.com/
http://www.geteasypeasy.com/