Sheila, it is quite obvious that the problem lies - as CarolC suggests - below/behind the tape slot, in the mechanism that turns the take-up spool. If, for any reason, the take-up spool can not keep up the pace of the tape (4,75 cm/sec) it results in what you were describing.

Adjusting or even replacing that mechanism (either belt or wheel driven) can be tricky and time-demanding, if not impossible because some brands seem not to provide any repair parts for cassette recorders at all.

Guest Russ here, sad to say, is quite right, thus my advice: if your player is not an expensive one and you don't want all your tapes to be damaged, buy a new one straight away. If it is, ask a repairer whether it'd be possible to fix it for a reasonable price - and then buy a new one :-)

AKS