  Based on the Ogorodnikov-Milne model, we analyze the proper motions of
Tycho-2 and UCAC2 stars. We have established that the model component that
describes the rotation of all stars under consideration around the Galactic y
axis differs significantly from zero at various magnitudes. We interpret this
rotation found using the most distant stars as a residual rotation of the
ICRS/Tycho-2 system relative to the inertial reference frame. For the most
distant ($d\approx900$ pc) Tycho-2 and UCAC2 stars, the mean rotation around
the Galactic y axis has been found to be $M_{13}=-0.37\pm0.04$ mas yr$^{-1}$.
The proper motions of UCAC2 stars with magnitudes in the range $12-15^m$ are
shown to be distorted appreciably by the magnitude equation in
$\mu_\alpha\cos\delta$, which has the strongest effect for northern-sky stars
with a coefficient of $-0.60\pm0.05$ mas yr$^{-1}$ mag$^{-1}$. We have detected
no significant effect of the magnitude equation in the proper motions of UCAC2
stars brighter than $\approx11^m$.
