What do you mean by "real time" here? I see two possible definitions here:
1) You want to transfer the files from one server to another as they are created and appended to
2) You want to be able to deterministically transfer a file from one computer to another in hard or soft realtime.
I'll focus on the latter as it is my area of expertise.
If you're looking to do the latter, and need hard (or close to hard) realtime, then I suggest RTNet
on Xenomai (for hard realtime). I don't think there's preexisting realtime file-transfer software, so you'll have to write your own.
For very soft realtime, you can just go with a dedicated Ethernet link and a standard Linux userspace process. You might be able to find a realtime-safe file transfer library for this application, too.
However, I don't think that this was the question you wanted answered, so please clarify your application so we can help you better.