I have two linux machine: redhat 7.3 and fedora core 2.
From redhat machine, I could access fedora machine using ssh. But could not access redhat machine from fedora. The message is "ssh: connect to host xx.xxx.xx.xx port 22: Connection refused".

The detailed verbose message are
OpenSSH_3.6.1p2, SSH protocols 1.5/2.0, OpenSSL 0x0090701f
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: Applying options for *
debug1: Rhosts Authentication disabled, originating port will not be trusted.
debug1: Connecting to 192.168.0.11 [192.168.0.11] port 22.
debug1: connect to address 192.168.0.11 port 22: Connection refused
ssh: connect to host 192.168.0.11 port 22: Connection refused

Thanks.

Is it possible you have a firewall rule blocking it?

I have tried both firewalls enabled with ssh and all other services on and using the same port. I also tried all firewalls turned off. But none of them are working. Is there other possibilities???

When you type:

telnet 192.168.0.11 22

Do you get the ssh version displayed?
or what happens when you:

ping 192.168.0.11

When I do telnet 192.168.0.11 22(or 23), telnet does not work.
The message is
Trying 192.168.0.11...
telnet: connect to address 192.168.0.11: Connection refused

When I do ping 192.168.0.11, it is working.
The message is
PING 192.168.0.11 (192.168.0.11) 56(84) bytes of data.
64 bytes from 192.168.0.11: icmp_seq=0 ttl=255 time=1.83 ms
64 bytes from 192.168.0.11: icmp_seq=1 ttl=255 time=0.124 ms
64 bytes from 192.168.0.11: icmp_seq=2 ttl=255 time=0.120 ms

When I do ssh 192.168.0.11, ssh does not work.
The message is
ssh: connect to host 192.168.0.11 port 22: Connection refused

Are you sure ssh deamon on the server side is running?

Since I can connet to my school site by ssh from both the machines, I believe ssh daemon is running.

Connecting is one thing but running the server is another. I mean you can use the ssh client on the machine your trying to connect to but really is the ssh deamon has to be running there. Try the command:
ps aux | grep ssh
And look for something like "/usr/sbin/sshd"
If you don't see anything this is the problem.
Let me know what you think.

Check whether sshd is running on your RedHat 7.3

#service sshd status

also check the /etc/hosts.allow and /etc/hosts.deny for any rules that block access.

sshd service need not be running if you want to use only the ssh client to connect to another machine. sshd service is required only when you want others to connect to your system.