Re-entrancy in multi-process applications.

I suppose this question isn't specific to C++, or even to C, but it's something I'm wondering about for a program I'm currently writing in C++, so I'll ask it here anyway.

In a multi-process application (using UNIX's fork()), it's perfectly okay for multiple children to call the same non-re-entrant library function, right? As in, non-re-entrancy is only a concern within a process (in signal handlers, exception handlers, etc.), right?

Thanks in advance for any information, relevant links, or the like.