Same as the previous question : the answer is big, "it depends."
Are you talking about classic ASP?
Sun had (has?) A product called "SunOne ASP" - although the product changed names so many times that I couldn’t say that it really was with the exception of the original ChiliSoft ASP product purchased and renamed Sun.
In any case, the above product will allow you to run ClassicASP / VBScript code on the * nix server and, for the most part, will work well. It was a little more fussy about some things, and there were certain things that didn't work perfectly right, but if you were leaning on it, you could make it work. Having said all this, I think that somewhere I read somewhere that the project was discontinued. Therefore, it may not be available.
There is also an Apache: ASP module, which (in my experience) only works with code written with it. If you are trying to port an application from a Windows server, its one of the options is "share your risk".
Are you talking about ASP.NET?
If so, you have a better chance ... the aforementioned Mono Project would be your best bet. He has come a long way since the last time I looked at him, but I did not have to install anything, I really can’t talk about how good / bad he is.
All things are equal ...
All things being equal, I would say that if you intend to use the MS programming language, run it on the MS server. It may cost a little more, but it will probably save you more headaches in the long run.
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