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The existence of free continental shelf waves in the Western Mediterranean Sea is studied using a statistical approach. Hourly mean sea level at six locations extended along the northern and southern coast of the Alborán Sea were analyzed by standard correlation and spectral analysis techniques for two periods of 91 and 92 days, respectively. The mean sea level was adjusted for the effect of atmospheric pressure according to the hydrostatic approximation. The wind-coherent response of sea level was removed by calculating the transfer function between the input alongshore wind stress and the output adjusted sea level. The cross-correlation analyses indicate time lags that are consistent with the hypothesis of the propagation of the free shelf waves predicted by the continental shelf wave theory. The presence of a westward-travelling signal on the NCS and a west-to-east travelling signal on the SCS of the Alborán Sea is confirmed. The cross spectra between residual sea level at the six locations show significant coherence at long periods. For these periods, the phase difference spectra show that the directions of propagation of the free waves are consistent with the interpretation of the cross correlation analysis. There is evidence of a seasonal variation in the phase speed of the waves, which may be related to variations in the speeds of currents in the Alborán Sea. The observations suggest the presence of continental shelf waves on both coasts of the Alborán Sea. [ABSTRACT FROM AUTHOR]