Abstract: In this paper the following Cauchy problem is under considerabon,
Lu=F(t,x₁,…,u,x_m,…,∂^m-1u) ∂^m-1u_t=0=q (j=1,…,m) where L is a strictly hyperbolic operator of m-th Order with respect to direction t, F is a C^∞ function of its arguments, the initial data have discontinuity along a smooth submanifold with codimentional 1 on initial plane and some conormal regularity with respect to manifold.