We explore the pattern of two-dimensional convection in an highly anisotropical porous medium. This physical situation is relevant to passive margin sedimentary basins consisting of interbedded coarse-grained previous and shale or limestone semi pervious layers, in particular to deltaic-type basins with sandstone lenses in a shale matrix. We show that permeability anisotropies of the order of 102--104 allow for long convective cells, of aspect ratio greater than 10, but that a combination of this parameter with a slight slope of the order of a few percent of the sedimentary layers is required to stabilize these long cells. As an example, we present the Okinawa basin, an active submarine back arc basin, with a sedimentary thickness of about 2 km and a heat flow profile across this basin, varying from 32 to 232 mWm-2 over a distance of 30 km. It is shown that this heat flow variation is diffucult to explain with conductive mechanisms only but is well reproduced by different convective models relying on permeability anisotropy plus slope. Although the insufficient thermal and structural constraints did not allow us to build a unique model, the whole set of possible fits to the heat flow data may restrict the mean hydraulic parameters of the basin. A vertical permeability of a few tens of millidarcy and an anisotropy greater than 100 are required to produce the expected stable and active large-scale circulation. It is suggested in clusion that this type of circulation might be active in oil-or ore-forming element migration. ¿ American Geophysical Union 1990