This paper states that a Gaussian process Y with mean 0 is equivalent to a Gaussian martingale starting from 0 if and only if Y is a semi-martingale with Gaussian martingale part and Gaussian “clrift” of a particular kind. We also obtain a theorem of Girsanov type tor Gaussian martingales and a criterion for the equivalence mentioned above in more convenient terms. Our results extend those of M. Hitsuda [8] concerning equivalence to a Wiener process