Theory of magneto-oscillation phenomena has been developed for two-dimensional electron systems with linear-in-k spin splitting. Both Dresselhaus and Rashba contributions are taken into account. It has been shown that the pattern of the magneto-oscillations depends drastically on the ratio between the above terms. The presence of only one type of the k-linear terms gives rise to the beats, i.e. two close harmonics corresponding to the spin-split subbands. However, if the strengths of both contributions are comparable, the third (central) harmonic appears in the spectrum of the magneto-oscillations. For equal strengths of the contributions, only the central harmonic survives, and the oscillations occur at a single frequency, although the k-linear terms remain in the Hamiltonian. Such suppression of the spin beats is studied in detail by the example of the Shubnikov-de Haas effect.