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In this paper, damping of the low frequency oscillations of multi-machine multi-UPFC power systems is investigated based on adaptive input-output feedback linearization control (AIFLC) approach. Considering a three-phase symmetrical fault, ignoring the subtransient states of the synchronous machines, the nonlinear state equations of the system are derived in order to obtain the UPFC reference control signals as well as the system parameters estimation laws. The stability of the system controller is proved by Lyapunov theory. Moreover using the six reduced order model of synchronous machine, some simulation results are presented in order to verify the validity and effectiveness of the proposed control approach.