Nonlinear solutal convection in a thin liquid layer driven by surface-tension gradients is studied. This effect is referred to as the Marangoni effect. The adsorbing ability of the upper surface is described by the Gibbs adsorption equation. The present analysis is based on the amplitude method, which allows for finite amplitude disturbances. The nonlinear terms are stabilizing or destabilizing according to the adsorption characteristics of the upper boundary. The present study generalizes earlier linear analyses. The nature of the convective pattern is also determined : it is shown that a hexagonal rather than a roll symmetry is expected.