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The main purpose of this paper is to investigate several further interesting properties of symmetry for the multivariate p-adic fermionic integral on ℤp. 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.