Why is a port closed on my router, but open on my modem?

I am trying to open a port on my computer. When connected directly to the broadband modem, the port is open. I have forwarded the port on the modem and it works just fine. However, when I tried to open the same port on my router, the port is closed again. Could having the same port forwarded on two different devices interfere with each other?

I am using Mac OS X 10.5.6 to make these changes.