Yes,
what user logons does each user use?
If they both use administrator, ensure that the
administrator password on both machines is the same.
Otherwise if they each have a different user account:
create the same user accounts and passwords on both
machines, this way 2000 will cache the password that was
used during logon for connecting to the other workgroup
machine. Ensure that both users reside in the admin
groups on both machines.
When you map a drive, click the reconnect at startup
button to cache the password.