High-mass X-ray pulsators are shown to be divisible into three groups on the basis of their observational properties: (i) the Be-star systems, (ii) non-Be-star systems with long pulse periods (∼102−103 s), and (iii) non-Be-star systems with short pulse periods (∼100−101 s). Differences in mass-transfer processes between the groups are invoked to account for the different properties. The separation of high-mass pulsators into three groups enables some of the properties of a pulsator to be predicted if only a few of its parameters are known. Because of this the optical counterparts of the X-ray sources H0850–42, 0A01653–40 and 1E1048.1–5937 are predicted to be either Be stars or, much less likely, low-mass binaries. The orbital (P0) and spin (PS) periods of the short-period systems may be anticorrelated; a phenomenon which is also exhibited by the intermediate polar white dwarf binaries. For the long-period systems there is no strong relationship between P0 and Ps as there is for the Be-star systems. It is shown that for the Be-star systems this relationship cannot be accounted for by accretion from a stellar wind if there is equality between the Alfvén and corotation radii of the neutron stars in these systems. However, accretion from a non-expanding atmosphere is not excluded. The lack of any correlation between PS and P0 for the supergiant systems is attributed to the low net angular momentum of accreted matter. The Be-star systems, however, probably accrete significant angular momentum which can result in an accretion disc.