The main purpose of this paper is to investigate several further interesting properties of symmetry for the multivariate p -adic fermionic integral on ℤ p . From these symmetries, we can derive some recurrence identities for the ζ -Euler polynomials of higher order, which are closely related to the Frobenius-Euler polynomials of higher order. By using our identities of symmetry for the ζ -Euler polynomials of higher order, we can obtain many identities related to the Frobenius-Euler polynomials of higher order.