Novel 1/B periodic low-field oscillations observed in the magnetoresistance of short-period lateral superlattices with weak electrostatic modulation are analyzed as being due to the formation of minibands. The energy gaps caused by the weak superlattice potential distort the Fermi circle of the unmodulated two-dimensional electron system (2DES) at the Brillouin-zone boundaries and form smaller closed Fermi contours giving rise to the novel oscillations. We discuss the periodicity of these novel oscillations for one-dimensional (1D) and two-dimensional (2D) lateral modulation and compare their dependence on the electron density with the well-known classical commensurability oscillations. (C) 2000 Elsevier Science B.V. All rights reserved.