The prediction of 5¿ mean gravity anomalies is considered by collocation from ATS 6/Geos 3 satellite to satellite range-rate observations. The auto- and cross-covariances of the residual line of sight accelerations ? from Geos 3 to ATS 6 are computed rigorously in the anomalous potential field. The raw residual range-rate ? values are filtered and smoothed by approximating them in a least-squares sense by a cubic spline function, and the residual accelerations ? are obtained as the first derivatives of the spline. Tests are described to fit the raw ? values by a spline function with variable knots, and to remove any linear trend from ? values due to residual errors in the initial state vectors. The correlation coefficients between the predicted values of neighboring anomalies are considered. The procedures are tested numerically by predicting eight 5¿ anomalies in the Carribean Sea area using destruct-Doppler data from four Geos 3 revolutions. The predicted anomalies are compared with anomalies obtained from altimeter data, with terrestrial anomalies, and with anomalies implied by the (30,28) PGS 110 gravitational model. In spite of a low density of range-range data directly over the anomalies, and the high noise level of the destruct-Doppler data, the tests indicate that 5¿ anomalies can be predicted with a standard deviation of 6 mgals. It is found that the predicted anomalies agree more closely with the altimeter anomalies as compared to the agreement of PGS 110 anomalies with the altimeter anomalies.