Washing machine won't fastspin at end of wash cycle

Hi.

I've a ca. 15 year old washing machine which works perfectly apart from a occasionally occuring fault which has cropped up recently. Being handy I'd prefer to fix it than scrap it for a new model (which don't seem to give anything like as much by way of reliable service)

What's happening is that at the end of it's cycle - at the point where it should enter the fastspinning phase, it doesn't. Rather, the drum just rotates at about 120 rpm for the rest of the cycle until the programme ends.

I've watched it when it's working correctly and the fastspin secton appears to be made up of 4 stages

slow spin (about the 120 rpm noted above)
medium fast for a while
pretty fast for a while
very fast for a short while
stop

When working normally you'll hear a sort of low,deep buzz from the machine as it cranks the motor up from the slow spin to the medium fast stage. When not working, you hear that same buzz, the drum appears to begin to start accelerating (or maybe that's my imagination), the buzz stops and the drum continues on at 120 rpm.

Any ideas?