Y. Imai and K. Iséki introduced two classes of abstract algebras: BCKalgebras and BCI-algebras ([2, 3]). It is known that the class of BCKalgebras is a proper subclass of the class of BCI-algebras. In [4, 5] Q. P. Hu and X. Li introduced a wide class of abstract algebras: BCH-algebras. They have shown that the class of BCI-algebras is a proper subclass of the class of BCH-algebras. J. Neggers and H. S. Kim introduced in [8] the notion of d-algebras, i.e. algebras satisfying (1) xx = 0, (5) 0x = 0, (6) xy = 0 and yx = 0 imply x = y, which is another useful generalization of BCK-algebras, and then they investigated several relations between d-algebras and BCK-algebras as well as some other interesting relations between d-algebras and oriented digraphs. Recently, Y. B. Jun, E. H. Roh and H. S. Kim introduced in [6] a new notion, called an BHalgebra, determined by (1), (2) x0 = x and (6), which is a generalization of BCH=BCI=BCK-algebras. They also defined the notions of ideals and boundedness in BH-algebras, and showed that there is a maximal ideal in bounded BH-algebras. J. Neggers and H. S. Kim introduced in [9] and investigated a class of algebras which is related to several classes of algebras of interest such as BCH=BCI=BCK-algebras and which seems to have rather nice properties without being excessively complicated otherwise. In this paper we discuss further relations between B-algebras and other topics, especially quasigroups. This is a continuation of [9].