The action observation network (AON) includes a system of brain areas largely shared with action execution in both human and nonhuman primates. Yet temporal and tuning specificities of distinct areas and of physiologically identified neuronal classes in the encoding of self and others' action remain unknown. We recorded the activity of 355 single units from three crucial nodes of the AON, the anterior intraparietal area (AIP), and premotor areas F5 and F6, while monkeys performed a Go/No-Go grasping task and observed an experimenter performing it. At the system level, during task execution, F6 displays a prevalence of suppressed neurons and signals whether an action has to be performed, whereas AIP and F5 share a prevalence of facilitated neurons and remarkable target selectivity; during task observation, F5 stands out for its unique prevalence of facilitated neurons and its stronger and earlier modulation than AIP and F6. By applying unsupervised clustering of spike waveforms, we found distinct cell classes unevenly distributed across areas, with different firing properties and carrying specific visuomotor signals. Broadly spiking neurons exhibited a balanced amount of facilitated and suppressed activity during action execution and observation, whereas narrower spiking neurons showed more mutually facilitated responses during the execution of one's own and others' action, particularly in areas AIP and F5. Our findings elucidate the time course of activity and firing properties of neurons in the AON during one's own and others' action, from the system level of anatomically distinct areas to the local level of physiologically distinct cell classes.