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Based on the Ogorodnikov-Milne model, we analyze the proper motions ofTycho-2 and UCAC2 stars. We have established that the model component thatdescribes the rotation of all stars under consideration around the Galactic yaxis differs significantly from zero at various magnitudes. We interpret thisrotation found using the most distant stars as a residual rotation of theICRS/Tycho-2 system relative to the inertial reference frame. For the mostdistant ($d\approx900$ pc) Tycho-2 and UCAC2 stars, the mean rotation aroundthe 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 $12-15^m$ areshown to be distorted appreciably by the magnitude equation in$\mu_\alpha\cos\delta$, which has the strongest effect for northern-sky starswith a coefficient of $-0.60\pm0.05$ mas yr$^{-1}$ mag$^{-1}$. We have detectedno significant effect of the magnitude equation in the proper motions of UCAC2stars brighter than $\approx11^m$.Comment: 15 pages, 6 figure

Kinematic control of the inertiality of the system of Tycho-2 and UCAC2 stellar proper motions