In this paper, the notion of generalized (Г,ϒ)-derivation determined by Г-derivation d is introduced on complicated subtraction (c-subtraction) algebra X and investigated some related properties in details. The c-subtraction algebra is a very important topic of subtraction algebra. If Г is an increasing function such that Г(x) ≤ Г(y) for all xϵX, then some equivalent condition are studied on the basis of generalized (Г,ϒ)-derivation determined by Г-derivation d on X.