For the Dirichlet problem on the k Hessian equation, Caffarelli-Nirenberg-Spruck (1986) obtained the existence of the admissible classical solution when the smooth domain is strictly k-1 convex in R^n. In this talk, we prove the existence of a classical admissible solution to a class of Neumann boundary value problems for k Hessian equations in strictly convex domain in R^n, this was asked by Prof.  N. Trudinger in 1987. The method depends upon the establishment of a priori derivative estimates up to second order. This is the joint work with Qiu Guohuan.