  We present an investigation of stellar proper motions of the TGAS catalogue
and ground-based HSOY, UCAC5 and PMA catalogues derived by combining with the
Gaia DR1 space data. This investigation concerns with only those stars of
ground-based catalogues that are contained in the TGAS. We analyze components
of the mutual rotation vector between these systems. It has been found that in
all three cases of comparison of the HSOY, UCAC-5 and PMA catalogues with TGAS,
the $\omega_{y}$ component of the mutual rotation vector depends on magnitude
nonlinearly within the range $9.5<m<11.5$, and has an amplitude reaching 1.5
mas/yr. The analysis has shown that the reason causing this effect is presence
in proper motions of the Tycho-2-stars containing in the TGAS, of some
inexplicable dependency on magnitude. It has been shown that proper motions of
the TGAS stars derived using AGIS differ from those derived as a result of
application the conventional (classical) method. At the same time, such a
difference in proper motions of Hipparcos-stars from TGAS derived by both
methods was not found. Investigation of systematic differences between proper
motions of the TGAS stars derived by the classical method and proper motions of
the HSOY, UCAC5 and PMA stars has shown that the values of the $\omega_{y}$
component in this case do not undergo any jumps and do not depend on magnitude.
That fact unambiguously indicates that some magnitude error is contained in
proper motions of Tycho2-stars derived by the use of AGIS. In the framework of
the solid-body rotation model the coordinate systems set by the TGAS catalogue
with classical proper motions (on the one hand) and by the HSOY, UCAC5 and PMA
catalogues (on the other hand) have mutual rotation with the components along
axis less than 0.2-0.3mas/yr.
