  Motivated by experiments, we study the sign of the Coulomb drag voltage in a
double layer system in a strong magnetic field. We show that the commonly used
Fermi Golden Rule approach implicitly assumes a linear dependence of
intra-layer conductivity on density, and is thus inadequate in strong magnetic
fields. Going beyond this approach, we show that the drag voltage commonly
changes sign with density difference between the layers. We predict that in the
Quantum Hall regime the Hall and longitudinal drag resistivities are
comparable. Our results are also relevant for pumping and acoustoelectric
experiments.
