One considers the context of the concurrent optimization of several criteria Ji(Y) (i=1,…,n), supposed to be smooth functions of the design vector Y∈RN (n⩽N). An original constructive solution is given to the problem of identifying a descent direction common to all criteria when the current design-point Y0 is not Pareto-optimal. This leads us to generalize the classical steepest-descent method to the multiobjective context by utilizing this direction for the descent. The algorithm is then proved to converge to a Pareto-stationary design-point.