The dispersion curve for fundamental-mode Love waves between periods of 60 and 4.375 sec has been obtained by the finite element method for a path normally incident at a continental margin (California) between a seismometer site on the ocean bottom 120 km from the continental shelf and a coastal seismographic station (Berkeley). Between periods of 60 and 17.5 sec, the computed phase velocity of fundamental-mode Love waves across the continental margin was very slightly greater (less than 1 per cent) than the mean of the phase velocities of fundamental-mode Love waves in the horizontally layered structures at the ends of the model representing the regions of the ocean bottom and continent. Between periods of 15 and 4.375 sec, the phase velocity of fundamental-mode Love waves across the finite element model was, in general, slightly less (about 2 per cent) than the mean of the phase velocities of fundamental-mode Love waves in the horizontally layered bounding structures. Two important new results concerning the propagation of the energy of fundamental-mode Love waves at a continental boundary were obtained. First, between periods of 20 and 11 sec, 90 per cent of the energy of fundamental-mode Love waves incident from the oceanic side is transmitted as the first higher mode. Second, between periods of 15 and 8 sec, only 2 per cent of the energy of fundamental-mode Love waves incident from either the oceanic or the continental side of the continental boundary is transmitted in waves of the fundamental Love mode. From the first of these results, it follows that, at periods of 20 sec or less, measurements on a continent of the phase velocity of fundamental-mode Love waves will be contaminated by the presence of the first higher mode. From the second, it follows that, between periods of 15 and 8 sec, the continental boundary is a barrier to the propagation of fundamental-mode Love waves in both directions, quite independently of damping. This strongly affects estimates of the attenuation of fundamental-mode Love waves. Fundamental-mode Love wave microseisms on the ocean floor from an oceanic source can be expected to be approximately four times as large as fundamental-mode Love wave microseisms from the same source at continental sites.