Is it illegal to post links on a website you own to a website containing illegal material?

Probably not illegal, but your question created more questions in my mind than answers. What kind of web site do you have? What does the link concern? Where is the link going, etc. Further, torrent sites often get swept into law suits with the people who link to them. You could be creating some liability for yourself when I know the answer to the other questions I though of. This is the kind of question I would rather discuss on the phone than try to answer based on the short scenario you posted. If you want to discuss your situation with a lawyer in more detail, most lawyers on offer a free phone consultation.

There is actually a case dealing with this. You CAN be considered to be encouraging or inciting people to break the law by directing them towards that site, in which you would be a contributor to the illegal activity (downloading). I don't recall the actual name of the case, but I would be extremely careful-- it's better just not to post.