Stimuli in simple oddball target detection paradigms cause evoked responses in brain potential. These responses are heritable traits, and potential endophenotypes for clinical phenotypes. These stimuli also cause responses in oscillatory activity, both evoked responses phase-locked to stimulus presentation and phase-independent induced responses. Here, we investigate whether phase-locked and phase-independent oscillatory responses are heritable traits. Oscillatory responses were examined in EEG recordings from 213 twin pairs (91 monozygotic and 122 dizygotic twins) performing a visual oddball task. After group Independent Component Analysis (group-ICA) and time-frequency decomposition, individual differences in evoked and induced oscillatory responses were compared between MZ and DZ twin pairs. Induced (phase-independent) oscillatory responses consistently showed the highest heritability (24–55%) compared to evoked (phase-locked) oscillatory responses and spectral energy, which revealed lower heritability at 1–35.6% and 4.5–32.3%, respectively. Since the phase-independent induced response encodes functional aspects of the brain response to target stimuli different from evoked responses, we conclude that the modulation of ongoing oscillatory activity may serve as an additional endophenotype for behavioral phenotypes and psychiatric genetics.