Let n 2 N. An additive map h : A ! B between algebras A and B is called n-Jordan homomorphism if h(an) = (h(a))n for all a 2 A. We show that every n-Jordan ho- momorphism between commutative Banach algebras is a n-ring homomorphism when n < 8. For these cases, every involutive n-Jordan homomorphism between commutative C-algebras is norm continuous.