The notion of generalized (regular) (${alpha},;{eta}$)-derivations of a BCI-algebra is introduced, some useful examples are discussed, and related properties are investigated. The condition for a generalized (${alpha},;{eta}$)-derivation to be regular is provided. The concepts of a generalized F-invariant (${alpha},;{eta}$)-derivation and ${alpha}$-ideal are introduced, and their relations are discussed. Moreover, some results on regular generalized (${alpha},;{eta}$)-derivations are proved.