A method for extracting periodic signals from altimeter data is applied in the Gulf of Mexico using data from the first two years of the Geosat Exact Repeat Mission. The least squares fitting of selected frequencies of sine and cosine functions to the time series of sea surface height at each point of the Geosat ground track is used to estimate the dominant frequency in the gulf for this time period. Optimal interpolation of the sine and cosine coefficients at the dominant frequency to a uniformly spaced grid allows reconstruction of the time series in the gulf and shows eddies shedding from the Loop Current with a period of approximately 10.5 months, consistent with shedding periods determined from numerical models and analysis of satellie infrared data. This technique is a novel method for investigation of periodic signals in Geosat altimetry and is not severely affected by the data outages present in the time series. ¿American Geophysical Union 1990