A consistent theory of magnetotransport and collision broadening for a two-dimensional electron system with a periodic modulation in one direction is presented. The theory is based on the self-consistent Born approximation for the scattering by randomly distributed short-range impurities and explains recent experiments which revealed, in addition to the familiar Shubnikovde Haas oscillations at stronger magnetic field, a new type of low-field oscillation, also periodic in B-1 but with a period depending on both the electron density and the period of the spatial modulation. It is shown that the antiphase oscillations observed for the resistivity components xx and yy have as a common origin the oscillating bandwidth of the modulation-broadened Landau bands, which reflects the commensurability of the period of the spatial modulation and the extent of the Landau wave functions. Recent magnetocapacitance experiments are also well understood within this theory. © 1990 The American Physical Society.