We classify, up to outer conjugacy, free actions of Z on an inclusion of hyperfinite type II1 factors of finite index, of finite depth, and for which the principal graph is one of the following: An, n ≥ 2, E6, E8, or a finite group. As a consequence, we obtain the classification of hyperfinite type IIIλ subfactors of the same index of the Powers factor Rλ, for 0 < λ < 1, such that the principal graph of the corresponding type II1 inclusion is of one of the types mentioned above. © 1996 Academic Press, Inc.