I wish to host same asp.internet application on 2 different servers under 2 different domains. To a back-up just in case among the servers malfunction. Is it feasible?

Sure it is possible. The secret is to make sure that the information stays synchronized, which isn't always easy going across domain names.

A much better approach may be to make use of Clustering. It's much more of a Network Administrator's task than the usual developer task (which means this may be beter clarified on ServerFault.com), but yes, it is possible.

Some articles on Clustering:

http://technet.microsoft.com/en-us/library/bb687537.aspx

http://technet.microsoft.com/en-us/library/bb742600.aspx

http://blogs.iis.internet/thomad/archive/2009/10/27/iis7-and-failover-clustering.aspx

Setup one domain title like a CNAME for that other. Then run both servers like a redundant cluster.

You will find points to consider within the application though: would you use sticky periods to ensure that a person having a session on a single server is definitely offered through the same one before session expires or are you able to rewrite the application to prevent session variables or then add mechanism to synchronise together...

Microsoft Support:How You Can: Setup Multi-Server ASP.Internet Web Programs and Web Services