The Teichmüller space is the space of marked Riemann surfaces of fixed topological type, and, with Teichmüller metric, it often behaves like a non-positively curved space. Every Teichmüller geodesic ray is given by a Riemann surface, its base point, and a measured foliation, its direction. Fixing a measured foliation, we discuss about the conditions for two Teichmüller geodesics rays from difference base points to be (strongly) asymptotic. This is joint work with Subhjoy Gupta.