The concept of derivation in a BF- algebra has been introduced . In addition a left –right anda right- left- derivation of BF2 algebras, left and right - derivation of ideal in BF− algebras are investigated. Different characterization of right-left-derivations,leftright - derivation,self map and fixed subalgebras have been discussed. We have also discussed derivation of BFalgebra if left and right –derivations are equal. In general different new theorems, Lemmas,Propositions and Corollaries have been proved.

Keywords : BCI-algebra,B-Algebra, BG- algebra, Derivation of B-algebra,and BF-algebra. Subject Classification Numbers: 06F35,47L45,08C05