Synthetic aperture radar has been used to image long-period (15--200 s) gravity waves in the nearshore region of Lake Michigan. These long-period waves are a response of the sea surface to forcing by a nonmonochromatic, wind-generated surface wave field. The synthetic aperture radar data were successfully compared with an in situ wave gauge record. Both one- and two-dimensional fast Fourier transforms were generated from near and offshore regions of synthetic aperture radar data. The synthetic aperture radar-derived near and offshore spectral estimates exhibited both low- and high-frequency wave components. Classical bathymetrically controlled wave refraction was observed for both the short as well as long wave components of the sea surface. This paper demonstrates the ability of X band synthetic aperture radar to low-amplitude, long-period signals. The signals appear to correspond to a 'surf beat' generated by the incident wind wave field.