Starts fine - engine pulses - then runs fine
 

New to forum - just purchased '89 cabrio 162,000 km - own an '07 gti.
This question has probably been asked a lot - sorry - didn't want to scroll through hundreds of postings (although it's kind of fun).
My '89 cabby starts fine, runs well for about 10 minutes and then the engine goes into a consistently rhythmic revving pattern - kind of lurches when driving . It does this for another 10 - 15 minutes and then runs perfectly fine after that.
What's happening?

Thanks all.

Engine cuts off while moving
 

My VW Polo 1.6 1997 model did cut of while driving. What could be the problem for me to fix the problem now while on duty. I don't wanna get stuck on my way back home