Disclaimer: I haven't solved the clues in the question, and obviously if I had I might think differently.
It looks to me -- perhaps wrongly -- as if these clues amount to this: "Local girl (4,4) gives smooth head (5,5)". (Of course that isn't a valid structure for an actual cryptic clue, but hopefully you see what I mean.) In terms of Hagen von Eitzen's answer, this feels much more like "X is son of Y" and "Y is father of X" rather than "y is x-3" and "x is 2y". Both clues are saying essentially the same thing.
This is more reliably bad in mathematics than it is in crosswords, and with a few cross-checking letters in hand these clues might become quite easy. It feels rather unkind, though.
I don't recall (though my memory is extremely fallible) ever seeing a pair of clues linked in this sort of way in an actual crossword. On the other hand, of course you do sometimes get a single clue whose solution is distributed between multiple spaces in the grid, so it's not like it's unheard of to have several spaces' worth of answer derived from a single piece of information.
For what little it's worth -- and, again, it's worth extra-little since I don't actually know how these clues work yet -- I don't think I would use these clues as they stand. Two mutually-referring clues giving two different relationships between their answers might be a different matter. (I would expect it to be difficult to come up with good clues of that sort.)
[EDITED to add:] Now Neil W has given us the solutions. Do I need to change any of the above? Well, I was right about the structure and about how the clues relate to one another, and I still dislike the redundancy. On the other hand, the fact that Neil found the solution -- fairly easily, if I'm understanding his comments right -- is evidence that the redundancy probably doesn't make the clues unfairly difficult. (And, knowing the answer, I agree that the first one seems like it shouldn't be too hard to think of.)