LetH = (V, E) be a hypergraph and let A be the E−V incidence matrix. We callH box-Mengerian if the linear system Ax ≥ 1, x ≥ 0 is box-totally dual integral (box-TDI). As it is NP -hard in general to recognize box-Mengerian hypergraphs, a basic theme in combinatorial optimization is to identify such objects associated with various problems. In this paper we show that the so-called ESP (equitable subpartion) property, first introduced by Ding and Zang in their characterization of all graphs with the min-max relation on packing and covering cycles, turns out to be even sufficient for box-Mengerian hypergraphs. We also establish several new classes of box-Mengerian hypergraphs based on ESP property. This approach is of transparent combinatorial nature and hence is fairly easy to work with. MSC 2000 subject classification. Primary: 90C10, 90C27, 90C57. OR/MS subject classification. Primary: Programming/graphs.