When you say you have the router address, is it something like 192.168.1.0?
If so, that's the routers address from INSIDE your home LAN.
You need the IP address provided by your ISP. It's listed in your router config or just go to:
Next step is punching a hole thru your firewall. You have to tell the firewall(usually built in to the router) to allow access on the filemaker port 591 or port 80.
Hope that helps/
Thank you very much for you hint. I had the rigth IP Adress. But you said right: I have to punch a hole into the firewall (or whatever). I tried many things. In the router configs I found the possibility to turn on static NAT-Address. That was the solution. I had to tell the router where to route (to which computer) someone accesses my network from outside. Now it works fine.But I just worry about the security issue. I had to turn off the mac firewall in the security system settings. I tried to add FileMaker Pro to the list to which access is allowed. It works only if firewall is completely turned off. Do you think that is dangerous?