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The nonlinear stability of the motionless state of a binary fluid mixture heated and salted from below, in the Oberbeck-Boussinesq scheme, for stress-free and rigid-rigid boundary conditions and Schmidt numbers PC greater than Prandtl numbers PT , is studied in the region around the bifurcation point &scriptC;02 = &scriptR;B2 (PT +1)/[PT (p-1)] of linear instability.An improvement of the results in Mulone [11] is found for small values of p = PC/PT and PT. For p suf.ciently large the critical nonlinear Rayleigh number is very close to the linear one (with relative difference less than 1% in the sea water case) [ABSTRACT FROM AUTHOR]