In the present paper, we propose a control strategy for the stabilization of a class of nonlinear cascade systems with input-dependent saturation. The saturation constraint considered is a constraint of order: the control input of one subsystem has to be smaller than the control input of the preceding subsystem of the cascade structure. This class of systems include interconnected reactors device such as multi-stage continuous fermentors. The control law is designed on the basis of a specific Lyapunov function previously introduced by R.Antonelli and A.Astolfi in [1]. It guarantees the stability of the closed-loop system, the convergence of the state variable to the set-point and the fulfillment of the saturation constraint all along the trajectories of the closed-loop system. The approach is applied, in numerical simulation, to a concrete example of a series of interconnected continuous bioreactors.