We prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras and of generalized derivations on real Banach algebras for the following Cauchy-Jensen functional equations: f ( x + y / 2 + z ) + f ( x − y / 2 + z ) = f ( x ) + 2 f ( z ) , 2 f ( x + y / 2 + z ) = f ( x ) + f ( y ) + 2 f ( z ) , which were introduced and investigated by Baak (2006). The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias' stability theorem that appeared in his paper (1978).