  We study the birationality (onto its image) of the Abel-Prym morphism
associated with a Prym-Tuyrin variety. We use such result to prove that Picard
bundles over Prym varieties are simple and moreover they are stable when the
Abel-Prym morphism is not birational. As a consequence we obtain that Picard
bundles over moduli spaces of stable vector bundles with fixed determinant are
simple. We prove that Picard bundles over moduli spaces of rank 2 vector
bundles on curves of genus 2 bundles are stable.
