Today I just ran a check of all my open ports with nmap and I found one unkown port open -- port no. 32768. So I tried to check the corresponding application which opened it by the command

netstat -nlp

but even this simply showed a dash in place of the process no. of the process listening on that port. The entry was something like this --

tcp 0 0 0.0.0.0:32768 0.0.0.0:* LISTEN -

Finally I tried fuser to get the process no.--

fuser -n tcp 32768

But it did not return anything at all which implies that that port is not opened by any application. Now how is this possible. How and why is that port open? How can I find out?

Try:

You can close the nfslock service; only if you are not exporting any NFS shares.
chkback again then for that port.

Its usually some kind of RPC program which opens such high ports...if not NFS like Amit suggested you might want to check whether you have any other RPC service like NIS running. Still though...I admit it doesnt completely answer why a port should remain open if an app hasnt opened it. I mean..shouldnt NFS(lockd , mountd , portmap...rpcgsvvd...whatever) have been assosciated with it. Or am I missing something???

Why don't you activate your firewall and make it log activity on port 32768 (2^15, that of any significance?)...

You can get information about rpc processes by using:
rpcinfo -p localhost