In this paper, we study the class of ortho-u-monoids which are generalized orthogroups within the class of E（S）-semiabundant semigroups. After introducing the concept of （-）-Green＇s relations, and obtaining some important properties of （-）-Green＇s relations and super E（S）-semiabundant semigroups, we have given the semilattice decomposition of ortho-u-monoids and a structure theorem for regular ortho-u-monoids. The main techniques that we used in the study are the （-）-Green＇s relations, and the semi-spined product of semigroups.
Assume that B is the variety of bands, and the identities of V∈l（B） involve n variables （n≥ 2）. In this paper, we show that V is Dn-1-testable and is not ：Dn-2- testable.
