ABSTRACT We present the first application of the vector spherical harmonics technique to the proper motions of the catalogues UCAC4, XPM and PPMXL for stars in the 11 to 17 mag range. The results obtained from the all-sky and from the Northern and Southern Galactic hemispheres solutions are discussed. The all-sky solution gave the parameters of the standard Ogorodnikov–Milne model (coordinates of the solar motion apex, the Oort constants, the angular speed of the local Galactic rotation, the slope of the local rotational velocity curve) which practically coincide with the traditional least-squares estimates. Essentially new is the fact that the all-sky vector spherical harmonics analysis detected the same strong and reliable extra-model harmonics in all the catalogues under consideration. In addition, the Northern and Southern hemisphere solutions (again in all the catalogues) gave the sign changes of the same Ogorodnikov–Milne parameters. It was shown that both effects are generated by the retardation of the