  The main purpose of this paper is to prove the smooth local orbital
linearization theorem for smooth vector fields which admit a complete set of
first integrals near a nondegenerate singular point. The main tools used in the
proof of this theorem are the formal orbital linearization theorem for formal
integrable vector fields, the blowing-up method, and the Sternberg-Chen
isomorphism theorem for formally-equivalent smooth hyperbolic vector fields.
