How can I fix my tape player?

I have a 1092 vintage JVC mini shelf system which I bought new. I have about 300 tapes. Everything works fine except the tape player. Both drives of the tape player are afflicted with the tendency to make a high pitch squeal thru the speakers intermittingly, about two thirds or so into a tape. The music continues even during the squeal. If I stop and restart the tape immediatley the squeal is gone until the next event. I have cleaned the heads. Any suggestions how to correct this will be appreciated. Ben Albritton