B-algebra is a non-empty set X with a constant 0 and a binary operation ∗ denoted by (X; ∗; 0), satisfying the certain axioms. A specialization of B-algebra is BM-algebra. Moreover, relation of B-algebra and BM-algebra is every BM-algebra is B-algebra, but its converse does not hold in general. In this thesis, discussed derivations and the generalized derivations of BM-algebras and B-a…