Generalized and lateralized periodic discharges have not been reported previously in the same EEG simultaneously. Here, we report two adult patients who suffered from rare clinical conditions [subacute sclerosing panencephalitis (SSPE) and nitochondrial myopathy, encephalopathy, lactic acidosis, and stroke-like episodes (MELAS) syndrome]. Their EEGs showed the same pattern consisting of generalized periodic discharges and lateralized periodic discharges in the same EEG simultaneously. Although the appearances of the EEG were very similar, discharges became more prominent after intravenous diazepam injection in the case with SSPE but were suppressed in the case with MELAS. Lesions in the magnetic resonance imaging (MRI) were located posteriorly in both patients, involving mainly subcortical white matter in the case with SSPE, but mainly the cortical area in the case with MELAS. Generalized periodic discharges are also reported in MELAS for the first time. The underlying mechanisms of the genesis of periodic discharges are still not known, and these two patients may help us to learn more about these rare patterns.