The overall objective of this study is to address questions concerning the longterm mechanical strength of the lithosphere across the equatorial margin of Brazil. The approach used in this study consists of calculating the frequency response function estimates, also called admittance, using gravity and bathymetry data. These experimental estimates are then compared to theoretical admittance curves for Airy and thin elastic plate models for which estimates on the flexural rigidity or, equivalently, effective elastic thickness may be made. Twelve profiles, each 256 km long, were extracted from gridded gravity and bathymetry data (data sources: project EQUANT, Defense Mapping Agency, National Geophysical Data Center files and GEOS 3/SEASAT altimeter data). Three profiles were specifically used for testing truncation errors introduced by four different data treatment procedures (before Fourier transforming the data) : detrending, applying 10% cosine tapering, mirror imaging and the use of the first derivatives. The method I adopted is similar to the one used by McNutt (1983) and consists of testing how reliably a given admittance estimate can be recovered as a function of the data treatment procedure. A "predicted" gravity anomaly was obtained by convolving each bathymetric profile with a theoretical admittance filter. The edges of this anomaly are then submitted to the same treatment as the corresponding bathymetric profile before Fourier transforming both profiles and calculating admittance. The stability of the long-wavelength admittance estimates, in the presence of noise, was also investigated by introducing Gaussian noise, in the range of -50 to +50 mGals, in the "predicted" gravity signal. The results indicate that relatively unbiased long-wavelength admittance estimates can be obtained by using the first derivative of the data sets. In addition, it is shown that the mirroring technique, used in previous admittance studies across Atlantic-type margins, leads to overestimated admittance values and, therefore, overestimated flexural rigidities. Neither the theoretical curves for the Airy model nor the plate flexure model can explain the experimental admittance estimates. Not only are the experimental admittance estimates higher than the predicted values but they also have a narrower peak than the theoretical curves. This raises the question of the applicability of highly simplified isostatic models for tectonic provinces such as Atlantic-type continental margins. The following reasons may explain the discrepancies between the experimental and theoretical admittance estimates (1) The abrupt nature of the transition between oceanic and continental crust controlled by the Romanche Fracture Zone - Unlike the eastern North American continental margin which was formed as a result of extensive rifling and pulling apart, the obliquely-rifled equatorial margin of Brazil has undergone a complex tectonic evolutionary process, where additional components such as shear and right-lateral wrenching were present. Therefore, representing the margin as a thin homogeneous elastic plate might be reasonable when the transition is gradual (for which the uniform flexural rigidity assumption seems reasonable) but is probably not a good approximation when it is as abrupt as the equatorial margin of Brazil (2) Presence of subsurface loads - Previous studies have shown that estimates of the average flexural rigidity of continental lithosphere using the admittance approach are biased when subsurface loads are present. In principle, the proximity of the Romanche Fracture Zone and associated volcanism suggest that shalow buried loads, caused by intrusive bodies, might be present in the area. This could partially account for the mismatch between theoretical curves and experimental admittance estimates. (3) "Masked" estimates - The admittance estimates presented here are likely to reflect the combination of two different signals: one related to the compensation of the Barreirinhas/Piaui-Camocim sub-basin which has no topographic/bathymetric expression and the other one related to the topography/bathymetry and its compensation which is of interest in the admittance studies. Since the wavelengths of these signals do not differ by much (around 80-100 km for the basin) it is possible that in the averaging process some overlaping occurs. The combination of these signals could yield anomalous results masking the admittance estimates in the diagnostic waveband. In addition, I present a two-dimensional cross section obtained by forward modelling the gravity anomaly along a profile using the line integral method. The uniform sedimentary infill of the Barreirinhas/Piaui-Camocim basin basin is enough to account for the gravity low over the inner shelf and no Moho topography is required. A plausible explanation for this "rootless" basin structure is that the lithosphere is capable of supporting the sediment infill load, and thus, has finite flexural rigidity (basin is locally uncompensated).