We consider several notions of regularity, including strong regularity, bounded relative units, and Ditkin’s condition, in the setting of vector-valued function algebras. Given a commutative Banach algebra A and a compact space X , let A be a Banach A -valued function algebra on X and let A be the subalgebra of A consisting of scalar-valued functions. This paper is about the connection between regularity conditions of the algebra A and the associated algebras A and A . That A inherits a certain regularity condition P to A and A is the easy part of the problem. We investigate the converse and show that, under certain conditions, A receives P form A and A . The results apply to tensor products of commutative Banach algebras as they are included in the class of vector-valued function algebras.