Abstract. In this paper we study the
hyperbolicity of some normal systems of first-order nonlinear partial differential
equations, to which some multidimensional Monge-Ampère equations have been
reduced in  (H. T. Ngoan and N. T. Nga, On the Cauchy problem for
hyperbolic Monge Ampère equation, Acta Math. Vietnam. 29 (2004),
281--298). We prove that when the dimension n 5
all these systems are weakly hyperbolic.