For the precise computation of geoid undulations the effect of the attraction of the atmosphere on the solution of the basic boundary value problem of gravimetric geodesy must be considered. This paper extends the theory of Moriz for deriving an atmospheric correction to the case when the undulations are computed by combining anomalies in a cap surrounding the computation point with information derived from potential coefficients. The correlation term is a function of the cap size and the topography within the cap. It reaches a value of 3.0 m for a cap size of 30¿, variations on the decimeter level being caused by variations in the topography. The effect of the atmospheric correction terms on potential coefficients is found to be small, reaching a maximum of 0.0055¿10-6 at n=2, m=2 when terrestrial gravity data are considered. The magnitude of this correction indicates that in future potential coefficient determination from gravity data the atmospheric correction should be made to such data.