•We studied the hemispheric asymmetry of oscillatory activity evoked by moving sounds.•The spectral perturbation (ERSP) and inter-trial phase coherence (ITC) were measured.•The spectral perturbations were stronger in the right hemisphere.•The delta-alpha ITC showed stronger contralaterality in the left hemisphere.•The asymmetry of motion-onset response was similar to that of ITC (“neglect model”). The present study investigates hemispheric asymmetry of the ERPs and low-frequency oscillatory responses evoked in both hemispheres of the brain by the sound stimuli with delayed onset of motion. EEG was recorded for three patterns of sound motion produced by changes in interaural time differences. Event-related spectral perturbation (ERSP) and inter-trial phase coherence (ITC) were computed from the time-frequency decomposition of EEG signals. The participants either read books of their choice (passive listening) or indicated the sound trajectories perceived using a graphic tablet (active listening). Our goal was to find out whether the lateralization of the motion-onset response (MOR) and oscillatory responses to sound motion were more consistent with the right-hemispheric dominance, contralateral or neglect model of interhemispheric asymmetry. Apparent dominance of the right hemisphere was found only in the ERSP responses. Stronger contralaterality of the left hemisphere corresponding to the “neglect model” of asymmetry was shown by the MOR components and by the phase coherence of the delta-alpha oscillations. Velocity and attention did not change consistently the interhemispheric asymmetry of both the MOR and the oscillatory responses. Our findings demonstrate how the lateralization pattern shown by the MOR potential was interrelated with that of the motion-related single-trial measures.