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This paper deals with state feedback control of chained systems based on a Nonlinear Model Predictive Control (NMPC) strategy. Chained systems can model many common nonholonomic vehicles. We establish a relation between the degree of nonholonomy and the minimum length of the control horizon so as to make the NMPC feasible. A necessary condition on the control horizon of NMPC is given and theoretically proved whatever the dimension of the chained system considered. This relation is used to design a NMPC-based control strategy for chained systems. One of the advantages of NMPC is the capability of taking into account the constraints on state and on control variables. The theoretical results are illustrated through simulations on a (2,5) chained system, describing a car-like vehicle with one trailer. Difficult motion objectives that require a lateral displacement are considered.