In this paper we globalize J. H. C. Whitehead's simple homotopy theory [17] by constructing a homotopy functor Wh from polyhedra to simplicial H-spaces, such that Whitehead's theory amounts to the calculation of
pi Wh(K), the arc-components of Wh (K). "Higher simple homotopy theory" is then concerned with the full homotopy type of Wh(K), for example, its higher homotopy groups.