A set of ≈8 million single stars of the UCAC3 catalogue has been analysed. It contains stars with reliable proper motions with not less than three epochs of observations used to compute the proper motion. Our main goal is to investigate the inertiality of the reference system defined by ‘good’ stars of the UCAC3 catalogue. The formalism of vectorial spherical harmonics has been applied to analyse the system of proper motions of the selected UCAC3 stars. A comparison between the results of solutions for several subsets of UCAC3 stars shows that the key parameters significantly change with stellar magnitudes, colours and average distances. The values of the components of the rigid-body rotation vector of the Hipparcos Celestial Reference Frame (HCRF) with respect to extragalactic sources were determined using ‘proper motions’ of more than 8000 galaxies of the UCAC3 catalogue. The values are ω1= 0.58 ± 0.15, ω2=−1.02 ± 0.15, ω3=−0.59 ± 0.17 mas yr−1 in galactic coordinates. Traces of the considerable magnitude equation are seen in the ‘proper motions’ of the UCAC3 galaxies. The most significant component derived from the analysis of the UCAC3 galaxies is ω2. It does not contradict the results of the analysis of the proper motions of selected stars (ω2=−1.09 ± 0.02 mas yr−1).