  We study Le Potier's strange duality conjecture for moduli spaces of sheaves
over generic abelian surfaces. We prove the isomorphism for abelian surfaces
which are products of elliptic curves, when the moduli spaces consist of
sheaves of equal ranks and fiber degree 1. The birational type of the moduli
space of sheaves is also investigated. Generalizations to arbitrary product
elliptic surfaces are given.
