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This paper introduces an adaptive voltage and frequency control method for inverter-based distributed generations (DGs) in a multi-microgrid (MMG) structure using distributed cooperative control and adaptive neural networks (ANN). First, model-based controllers are designed using the Lyapunov theory and dynamics of the inverter-based DGs. ANNs are then utilized to approximate these dynamics, resulting in an intelligent controller, which does not require a priori information about DG parameters. Also, the proposed controllers do not require the use of voltage and current proportional-integral controllers normally found in the literature. The effectiveness of the proposed controllers are verified through simulations under different scenarios on an MMG test system. Using Lyapunov analysis, it is proved that the tracking error and the neural network weights are uniformly ultimately bounded, which results in achieving superior dynamic voltage and frequency regulation. [ABSTRACT FROM AUTHOR]