Objective: Electroencephalography (EEG) features in the alpha band have been shown to differ between people with epilepsy and healthy controls. Here, in a group of patients with mesial temporal lobe epilepsy (mTLE), we seek to confirm these EEG features, and using simultaneous functional magnetic resonance imaging, we investigate whether brain networks related to the alpha rhythm differ between patients and healthy controls. Additionally, we investigate whether alpha abnormalities are found as an inherited endophenotype in asymptomatic relatives. Methods: We acquired scalp EEG and simultaneous EEG and functional magnetic resonance imaging in 24 unrelated patients with unilateral mTLE, 23 asymptomatic first-degree relatives of patients with mTLE, and 32 healthy controls. We compared peak alpha power and frequency from electroencephalographic data in patients and relatives to healthy controls. We identified brain networks associated with alpha oscillations and compared these networks in patients and relatives to healthy controls. Results: Patients had significantly reduced peak alpha frequency (PAF) across all parietal and occipital electrodes. Asymptomatic relatives also had significantly reduced PAF over 14 of 17 parietal and occipital electrodes. Both patients and asymptomatic relatives showed a combination of increased activation and a failure of deactivation in relation to alpha oscillations compared to healthy controls in the sensorimotor network. Interpretation: Genetic factors may contribute to the shift in PAF and alterations in brain networks related to alpha oscillations. These may not entirely be a consequence of anti-epileptic drugs, seizures or hippocampal sclerosis and deserve further investigation as mechanistic contributors to mTLE.