Tomcat hanging -- Linux / Java problem?

I've written some webapps for internal use at the company where I work; they are deployed under Tomcat and seem to be working fine except that sometimes Tomcat hangs (not just a webapp). I looked at thread dumps -- the lockup seems to happen at random places... This is difficult to toubleshoot because it happens quite rarely. I haven't tried any stress tests yet...

This only happens on the "production" machine, which is running Red Hat Linux,kernel version 2.4.20. My development machine is running Windows 2000.

I tried Tomcat versions 4.1.18 and 5.0.16, JRE versions 1.3.something and 1.4.2_04-b05, and the problem is still there.

I suspect that this has something to do with the Linux / JVM compatibility. Do you know of any such issues and what would you recommend?