  We study the Einstein relation between diffusion and response to an external
field in systems showing superdiffusion. In particular, we investigate a
continuous time Levy walk where the velocity remains constant for a time \tau,
with distribution P(\tau) \tau^{-g}. At varying g the diffusion can be standard
or anomalous; in spite of this, if in the unperturbed system a current is
absent, the Einstein relation holds. In the case where a current is present the
scenario is more complicated and the usual Einstein relation fails. This
suggests that the main ingredient for the breaking of the Einstein relation is
not the anomalous diffusion but the presence of a mean drift (current).
