Is it possible, will it run well? Are there any limitations?

Is it possible, will it run well? Are there any limitations?
Short answer: Yes, probably not, and yes.

There's Sun's Chilisoft ASP and a Perl ASP extension and perhaps others.

Use Windows if you want to develop ASP apps.

I would recommend you to use Windows for ASP applications. However if you want to host your sites on the Linux server, I suggest you to host them on the server with Plesk installed because it has Sun's Chilisoft ASP plugin.

You can even work with ASP.NET if the Linux server has Mono compiler. But to get access all the features you should go for a Windows server.

You can try this

http://www.apache-asp.org/install.html

But frankly as those mentioned above, ASP emulation does not work really well in Linux.