Let be a near ring. An additive mapping : → is said to be a right generalized (resp., left generalized) derivation with associated derivation on if ( ) = ( ) + ( ) (resp., ( ) = ( ) + ( )) for all , ∈ . A mapping : → is said to be a generalized derivation with associated derivation on if is both a right generalized and a left generalized derivation with associated derivation on . The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations.