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 methods depends upon the establishment of a priori derivative estimates up to second order.  This is the joint work with Qiu Guohuan.

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