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We consider BCC-algebras as a generalization of BC K-algebras and prove that for any cardinal n> 4 there ex-ists a BCC-algebra with n elements which is not a BCK-algebra. Some methods of constructions of such BCC-algebras are given. In the end of this paper we consider some quasivarieties and va-rieties which are contained in the cłass of all BCC-algebras.

1. Introduction. As is shown by the title of the first paper on this subject [5], much of the work on BCK and related algebras was motivated by known work on implicational logic. This is illustrated by the similarities between the names of some of the systems. We have BCI-algebra and BCI positive logic, BCK-algebra and BCK positive logic, Positive implicative BCK-algebra and Positive implicative logic and Implicative BCK-algebra and Implicative (classical) logic.