Gravitational gliding of uppermost sediments down a passive margin is possible if there is a basal layer of evaporite or other soft material to allow detachment. In examples from the Gulf of Mexico and the Brazilian margin, gliding has produced three main structural domains: an uppermost domain of downdip extension; an intermediate domain of rigid gliding; and a lowermost domain of downdip contraction. Domain boundaries are established by changes in slope. In this paper, we examine three kinds of gravitational gliding, depending on the paths followed by material particles. In ideal parallel gliding, particle paths are parallel straight lines, trending downslope. This should occur where the margin is perfectly straight. In ideal radial gliding, particle paths are radii of a circle and the margin is shaped like a circular cone. Natural margins will not have ideal shapes; but divergent gliding will tend to occur off coastal salients; convergent gliding, off coastal re-entrants. A simple kinematic model based on ductile behaviour illustrates some essential features of radial gliding. Changes in radius during divergent gliding produce strike-parallel extension; during convergent gliding, they produce strike-parallel contraction. Vertical strains also differ. Divergent gliding produces an uppermost domain of strong vertical thinning, balanced by extensions in all horizontal directions. Similarly, convergent gliding produces a lowermost domain of strong vertical thickening, balanced by contractions in all horizontal directions. These deformed states cannot be restored by simple techniques based on section balancing. We have done three experiments using analogue materials: sand, to model the brittle behaviour of sediments; silicone putty, to model the ductile behaviour of basal layers of evaporite. The experiments were properly scaled to account for gravitational forces. Experiment I reproduced convergent gliding above a basement with a conical upper surface. Strike-parallel contraction was responsible for radial folds on the lower slopes. The lowermost domain had a complex fold pattern, indicating contraction in all horizontal directions. Experiment 2 reproduced divergent gliding above a basement with a pyramidal upper surface. Strike-parallel extension produced radial rifts on the upper slopes. The uppermost domain had a complex polygonal pattern of normal faults, indicating extension in all horizontal directions. Experiment 3 also reproduced divergent gliding, but due to non-uniform sediment thickness. We have examined the many seismic profiles, both downdip and alongstrike, available for the Brazilian margin. Alongstrike profiles show structures which we attribute to strike-parallel strains. Around the Santos re-entrant, syn-sedimentary growthfolds indicate strike-parallel contraction, increasing downslope. This argues for a mechanism of convergent gliding. In contrast, around the Campos salient, normal growth faults and associated salt rollers indicate strike-parallel extension, decreasing downslope. This argues for a mechanism of divergent gliding. The pattern of oil fields in the Campos area, including the giant Marlim field, seems to be closely controlled by divergent gravitational gliding and associated processes. Radial gliding should occur on other passive margins as well, especially where the coastline is sinuous. Structures around the western Gulf of of Mexico seem to indicate convergent gliding at the scale of the entire Gulf. Structures at a smaller scale around the Mississippi delta seem to indicate divergent gliding.