Please do not blame on me for bringing that question here but after days of searching in Internet for the answer I gave up and desided to ask the question myself.

I have VNC running on Redhat 9.0. When I try to connect with VNC client in my internal network (addresses 192.xxx...) I can connect with no problems. But if I try to connect from the external world or even in internal network by giving external IP my connection fails with an error Connection refused (10061).
My internal network stays behind a hardware firewall/router so the most obvious thing to look after would be the router settings. On the router connected to CableModem I opened the ports 5900, 5901, 5800, 5801, 21, 22 and forwarded them to the same port numbers of the internal IP of my Redhat. On the Redhat (RH) box I disabled the firewall at all.
From outside I can connect to Telnet(21) or SSH(22) but for some reason it fails to connect to VNC. From the client I tried to specify "24.xxx.xxx.xxx:5900", "24.xxx.xxx.xxx:5901", "24.xxx.xxx.xxx:0", "24.xxx.xxx.xxx:1", "24.xxx.xxx.xxx:5800", "24.xxx.xxx.xxx:5801" and nothing works.
I even tried to put my RH to demilitarized zone (DMZ) so the external IP is mapped to RH internal IP but the connection still fails.

Any suggestions what to try else?

Thank you

I forgot to mention that if I try to connect to Redhat VNC from the same box by giving the internal IP everything works fine but with the external IP it fails with the same error.

Actually it is a good thing that this is failing because connecting directly to VNC over the internet is a horrible breach of security. VNC transmits EVERYTHING (including passwords) in clear text.

So, what you really want to do is learn how to set up an SSH tunnel that VNC will work through. Since you can already connect via SSH, this should solve your problem. If you do a search here, you'll find dozens of threads on how to run VNC over an SSH tunnel.

2 Hangdog42

VNC over SSH works fine, thank you for the advise but I still do not understand why the direct connection doesnot work if all the necesary ports are open.

I agree, from what you've posted it should work with a direct connection. The only thing I can guess is that somehow the port forwarding isn't quite right. You really should only have to forward one port for each screen you've got running on VNC. You've disabled the firewall, so that isn't it and if you can run VNC over an SSH tunnel, then VNC is working right. About the only thing left is the port forwarding.