In this paper, long- and short-period vibrations in sedimentary basins are studied. First, two-dimensional, long-period vibrations of deep semi-circular basins for excitation by earthquake faults, which can be inside or outside the basin, are analyzed. Second, recurring intermediate peak frequencies of Fourier-spectrum amplitudes of recorded accelerations along the east-west axis of the San Fernando Valley during the 1994 Northridge, California earthquake are reviewed. It is shown that these intermediate frequencies cannot be associated with vibrations of the entire San Fernando basin because the frequency range of typical strong-motion recordings (0.04 to 15.0 s) is too narrow to include the long-period vibration of the whole basin. These intermediate vibrations are consistent with Kanai's one-dimensional models consisting of parallel layers and excited by vertically incident shear waves. (C) 2014 Elsevier Ltd. All rights reserved.