  We show that for a fixed curve $K$ and for a family of variables curves $L$,
the number of $n$-Poncelet pairs is $\frac{e (n)}{2}$, where $e(n)$ is the
number of natural numbers $m$ smaller than $n$ and which satisfies mcd $
(m,n)=1$. The curvee $K$ do not have to be part of the family.
  In order to show this result we consider an associated billiard
transformation and a twist map which preserves area.
  We use Aubry-Mather theory and the rotation number of invariant curves to
obtain our main result.
  In the last section we estimate the derivative of the rotation number of a
general twist map using some properties of the continued fraction expansion .
