Probably perished rubber parts.
The rubber pinch roller is responsible for pulling the tape past the head at a precise speed and that is also (in the the vast majority of cases) driven by a belt.
As these parts wear, pressure on the tape is lost and the take-up spool starts to pull the tape unhindered.
It will need a proper service but sadly that isn't cheap these days.
Just as an afterthought, it is possible that the pinch roller is very dirty causing the tape to slip, so try giving that a good clean with isopropyl alcohol.