Excessive daytime sleepiness (EDS) is one of the main symptoms of several sleep-related disorders with a great impact on patient lives. While many studies have been carried out in order to assess daytime sleepiness, automatic EDS detection still remains an open problem. In this work, a detection approach based on the time-frequency analysis of electroencephalography (EEG) signals is proposed. Multichannel EEG signals were recorded during five maintenance of wakefulness (MWT) and multiple sleep latency tests alternated throughout the day from patients suffering from sleep-disordered breathing. A group of 20 patients with EDS was compared with a group of 20 patients without daytime sleepiness (WDS) by analyzing 60-s EEG windows in the waking state. Measures obtained from the Choi-Williams distribution (CWD) and the cross-CWD were calculated in the EEG frequency bands delta (0.1-4 Hz), theta (4-8 Hz), alpha (8-12 Hz), beta (12-30 Hz), and total band (TB, 0.1-45 Hz). Statistical differences between EDS and WDS groups were found in the delta and theta bands during MWT events (p < 0.0001). The results show that the EDS group presented more power in the theta band, while the WDS group presented higher spectral and cross-spectral entropy in the frontal zone in the delta band. In general, CWD and cross-CWD measures yielded sensitivities and specificities of above 80 %. The area under the receiver operating characteristic curve was above 0.85 for classifying EDS and WDS patients.