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.