Let [Formula: see text] be a finite Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra [Formula: see text], the conformal quasiderivation algebra [Formula: see text] and the generalized conformal derivation algebra [Formula: see text]. The generalized conformal derivation algebra is a natural generalization of the conformal derivation algebra. Obviously, we have the following tower [Formula: see text], where [Formula: see text] is the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal [Formula: see text]-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal [Formula: see text]-derivations. In addition, all conformal [Formula: see text]-derivations of finite simple Lie conformal algebras are characterized.