In this paper, we investigate some fundamental properties and establish some results of f-derivations of BCI-algebras. Also, we prove Der(X), the collection of all f-derivations, form a semigroup under certain binary operation. 1. Introduction and preliminaries BCI-algebra has been developed from BCI-logic on the similar way as Bool- ean algebra was developed from Boolean logic which have a lot of application in computer sciences ((14)). Recently greater interest has been developed in the derivation of BCI-algebras, introduced by Y. B. Jun and X. L. Xin (8), which was motivated from a lot of work done on derivations of rings and Near rings (see (9, 11)). The notion was further explored in the form of f-derivations of BCI-algebras by J. M. Zhan and Y. L. Liu (15). In this paper, we prove some results on f-derivations of BCI-algebras. First, we show that an f-derivation of BCK-algebra is regular. However, we are able to show that under certain conditions namely, for a 2 X,f(a)⁄df(x) = 0 or df(x)⁄f(a) = 0, for all x 2 X the f-derivation, df, of a BCI-algebra X is regular and X is a BCK-algebra. Also, we study derivations in a p-semisimple BCI-algebra and show that if df,d 0 f are f-derivations in X, then df - d 0