Magnetoencephalographic and electroencephalographic evoked responses are primary real-time objective measures of cognitive and perceptual processes in the human brain. Two mechanisms (additive activity and phase reset) have been debated and considered as the only possible explanations for evoked responses. Here we present theoretical and empirical evidence of a third mechanism contributing to the generation of evoked responses. Interestingly, this mechanism can be deduced entirely from the characteristics of spontaneous oscillations in the absence of stimuli. We show that the amplitude fluctuations of neuronal alpha oscillations at rest are associated with changes in the mean value of ongoing activity in magnetoencephalography, a phenomenon that we term baseline shifts associated with alpha oscillations. When stimuli modulate the amplitude of alpha oscillations, baseline shifts become the basis of a novel mechanism for the generation of evoked responses; the averaging of several trials leads to a cancellation of the oscillatory component but the baseline shift remains, which gives rise to an evoked response. We propose that the presence of baseline shifts associated with alpha oscillations can be explained by the asymmetric flow of inward and outward neuronal currents related to the generation of alpha oscillations. Our findings are relevant to the vast majority of electroencephalographic and magnetoencephalographic studies involving perceptual, cognitive and motor activity.