Log shipping copy job failing

I have an issue with the LS COPY job for log shipping from Server A (primary) toServer B (secondary) -
Message

2012-12-24 13:00:06.95  *** Error: Logon failure: unknown user name or bad password.

(mscorlib) ***

2012-12-24 13:00:06.95  ----- END OF TRANSACTION LOG COPY     -----

Exit Status: 1 (Error)

However, the SQL agent account has FULL permissions on the log backup folders (BACKUP shares) on both primary and secondary servers. This is the service accountunder which SQL services run on both these servers.

Also, I noticed that when I try to connect to both these instances from outside the server (remotely), I get the SSPI context error:

"Cannot generate SSPI context"

I have tried to grant explicit permissions on the Backup folders on both servers.  Also, added the service account explicitly to
the SQLServerMSSQLUser$ServerA SQLServerSQLAgentUser$ServerB local groups.But did not help.

Can someone please help?

Any help is highly approeciated!!..

Thanks.