Cross-special techniques have been used to analyze the relationship between gravity and bathymetry on 26 profiles across the Walvis and Ninetyeast ridges. The resulting filters or transfer functions have been used to study the state of isostasy at these ridges. Transfer functions for the eastern Walvis Ridge and the Ninetyeast Ridge profiles can be best explained by an Airy-type thickening of the crust beneath these ridges. The crustal thicknesses required are in the range 15--25 km, in good agreement with available seismic refraction data. The transfer function for the western Walvis Ridge can be best explained by a flexure model in which the oceanic lithosphere is treated as a thin elastic plate overlying a weak fluid. The effective elastic plate thickness required is in the range 5--8 km. These estimates for the elastic thickness are substantially less than those determined from flexural studies of loads on older crust but are similar to estimates determined for sea floor topography at midocean ridges. These observations are consistent with the formation of aseismic ridges near spreading centers on lithosphere that is young, thin, and relatively weak. The differences in isostasy between the eastern and western Walvis Ridge are attributed to an off-axis shift relative to the South Atlantic spreading center of the 'hot spot' forming the Walvis Ridge about 80 m.y. B.P. These observations suggest that the isostatic parameters determined for these aseismic ridges were 'frozen in' at the time of their formation at or near a spreading center and have not significantly changed through time.