Question about Oracle processes parameter

I have a question about Oracle processes. It seems like I do not understand the behavior of processes parameter.

We have been running for several years an application that accesses an Oracle 10.2.0.5 instance running on Sun-Fire-880 (8cpus). This instance has processes=300 and it's been working fine for years.

We got a new system - Sun-Fire-T200 with 32 cpus. I created a new 10.2.0.5 instance and used impdp to copy the data. Testing this new environment we are getting problems with not enough processes. So I increased the processes to 800 and it seems to work fine (so far, we're still testing). I've been checking on the number or processes on this machine and I can see increasing processes (using ps -ef | grep oracle | wc).