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simple question


Dear Sirs:
I have a function whose output is of the form {{a,b,c},{d,e,f},k}
 
That is, a list of length 3, of which the first two parts are lists and the last part is a number
 
Now, I want to iterate it, with the following termination criterion: stop if the first two parts of the output are identical in two successive runs.
 
The intuitive (or naively intuitive if you want) way of attacking the problem, I think, is the following:
 
NestWhile[f,startinglist,UnsameQ[{#[[1]],#[[2]]}&,2]
 
But it does not work.
 
What is the solution?
Fg


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