Several authors have introduced sequential relaxation techniques – based on linear and/or semi-definite programming – to generate the convex hull of 0-1 integer points in a polytope in at most n steps. In this paper, we introduce a sequential relaxation technique, which is based on p-order cone programming (1≤p≤∞). We prove that our technique generates the convex hull of 0-1 solutions asymptotically. In addition, we show that our method generalizes and subsumes several existing methods. For example, when p=∞, our method corresponds to the well-known procedure of Lovász and Schrijver based on linear programming. Although the p-order cone programs in general sacrifice some strength compared to the analogous linear and semi-definite programs, we show that for p=2 they enjoy a better theoretical iteration complexity. Computational considerations of our technique are discussed.