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Conservation laws for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are studied.We propose a new differential variational principle,called the Pfaff-Birkhoff-dAlembert principle of Herglotz type.Birkhoffs equations for both the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are obtained.According to the relationship between the isochronal variation and the nonisochronal variation,the conditions of the invariance for the Pfaff-Birkhoff-dAlembert principle of Herglotz type are given.Then,the conserved quantities for the Birkhoffian system and the constrained Birkhoffian system of Herglotz type are deduced.Furthermore,the inverse theorems of the conservation theorems are also established.