For more than 20 years, a program has been underway to obtain records of earthquake shaking on the seafloor at sites offshore of southern California, near oil platforms. The primary goal of the program is to obtain data that can help determine if ground motions at offshore sites are significantly different than those at onshore sites; if so, caution may be necessary in using onshore motions as the basis for the seismic design of oil platforms. We analyze data from eight earthquakes recorded at six offshore sites; these are the most important data recorded on these stations to date. Seven of the earthquakes were recorded at only one offshore station; the eighth event was recorded at two sites. The earthquakes range in magnitude from 4.7 to 6.1. Because of the scarcity of multiple recordings from any one event, most of the analysis is based on the ratio of spectra from vertical and horizontal components of motion. The results clearly show that the offshore motions have very low vertical motions compared to those from an average onshore site, particularly at short periods. Theoretical calculations find that the water layer has little effect on the horizontal components of motion but that it produces a strong spectral null on the vertical component at the resonant frequency of P waves in the water layer. The vertical-to-horizontal ratios for a few selected onshore sites underlain by relatively low shear-wave velocities are similar to the ratios from offshore sites for frequencies less than about one-half the water layer P-wave resonant frequency, suggesting that the shear-wave velocities beneath a site are more important than the water layer in determining the character of the ground motions at lower frequencies.