In our social environment, we easily distinguish stimuli caused by our own actions (e.g., water splashing when I fill my glass) from stimuli that have an external source (e.g., water splashing in a fountain). Accumulating evidence suggests that processing the auditory consequences of self-performed actions elicits N1 and P2 ERPs of reduced amplitude compared to physically identical but externally generated sounds, with such reductions being ascribed to neural predictive mechanisms. It is unexplored, however, whether the sensory processing of action outcomes is similarly modulated by action observation (e.g., water splashing when I observe you filling my glass). We tested 40 healthy participants by applying a methodological approach for the simultaneous EEG recording of two persons: An observer observed button presses executed by a performer in real time. For the performers, we replicated previous findings of a reduced N1 amplitude for self- versus externally generated sounds. This pattern differed significantly from the one in observers, whose N1 for sounds generated by observed button presses was not attenuated. In turn, the P2 amplitude was reduced for processing action- versus externally generated sounds for both performers and observers. These findings show that both action performance and observation affect the processing of action-generated sounds. There are, however, important differences between the two in the timing of the effects, probably related to differences in the predictability of the actions and thus also the associated stimuli. We discuss how these differences might contribute to recognizing the stimulus as caused by self versus others.