abstract: Nelli and Rosenberg proved that, given a Jordan curve C contained at the boundary of H2xR at infinity, projecting one to one over the boundary of H2, then there is a minimal disk whose asymptitic boundary is C (and it is a vertical graph). We consider the problem of prescribing two such Jordan curves at infinity and look for a minimal annulus whose asymptotic boundary consists of the union of these two curves. In this talk we will discuss some existence and non-existence results for that problem. This is a joint work with Leonor Ferrer, Francisco Martı́n and Rafe Mazzeo.