This paper deals with the classification of the metabelian p-groups of maximal class and order pl where p is odd and, roughly, n _ 2p. This paper deals with the classification of the metabelian p-groups of maximal class and order pl where p is an odd prime and, roughly, n _ 2p. It also contains a result on the order of the automorphism groups of these groups. Some descriptive material must be developed before the main results, Theorems 4 to 8 below, can be stated. To begin let G be a group, G2= [G, G] be the commutator subgroup of G, and Gi+1 = [Gi, G] for i ?2. Then, by definition, G is metabelian if G2 is abelian. The group G, of order pn, is of maximal class if G > G2 > ... > Gn = 1 where I G: G21 =p2 and I Gi: Gi + 1 l =p for i = 2, 3,. . ., n-1. If G is of maximal class the subgroup G1 is defined by: G1 is the largest subgroup of G such that [G1, G2] p+1. Then [Gl, Gi] _ Gn-p+il i =1 2, .1 ..,p. This follows from Theorem 3.10 of [1] and the fact that GIG2 is elementary abelian. If we take i= 2 in Theorem 1 we get [G1, G2] ? Gn_ -p +2. Thus, by the general theory, there is an integer k with 0? k ?p -2 such that [G1, G2] = Gn k, and this integer k is an invariant of the group G. The structure of the groups in question can be described in terms of this invariant k. We have THEOREM 2. Let G be a metabelian p-group of maximal class and order pn where n > p + 1, and suppose that [G1, G2] = Gn k where 0 < k p -2. Let s be an element of G not in G1, Si be an element of G1 not in G2, and si= [si-1, s] for i=2, 3,. .., n. Received by the editors October 30, 1969. AMS subject classifications. Primary 2027, 2040.