  We consider the oscillating sign of the drag resistivity and its anomalous
temperature dependence discovered experimentally in a bi-layer system in the
regime of the integer quantum Hall effect. We attribute the oscillating sign to
the effect of disorder on the relation between an adiabatic momentum transfer
to an electron and the displacement of its position. While in the absence of
any Landau level mixing a momentum transfer $\hbar \bf q$ implies a
displacement of $ql_H^2$ (with $l_H$ being the magnetic length), Landau level
mixing induced by short range disorder adds a potentially large displacement
that depends on the electron's energy, with the sign being odd with respect to
the distance of that energy from the center of the Landau level. We show how
the oscillating sign of drag disappears when the disorder is smooth and when
the electronic states are localized.
