We determine the solutions f : S → H of the generalized Jensen’s functional equationf (x + y) + f (x + φ(y)) = 2f (x),    x,y ∈ S,and the solutions f : S → H of the generalized quadratic functional equationf (x + y) + f (x + φ(y)) = 2f (x) + 2f (y), x,y ∈ S,where S is a commutative semigroup, H is an abelian group (2-torsion free in the first equation and uniquely 2-divisible in the second) and φ is an endomorphism of S.