The successful processing of baseline vectors is an essential step toward the application of GPS surveying techniques to leveling. When carrier phase observables are used, the double-difference integer phase ambiguity parameters must be correctly resolved. It is described how the phase ambiguities are resolved with ionospheric-free signals using standard procedures. With the dual-frequency phase data from satellite surveying ih rapid static mode baseline vectors of up to 26 km can be solved. A standard deviation in the vertical component of about 2.5 cm can usually be expected for a baseline length of less than 10 km. The accuracy of the height determination by means of GPS relative positioning is then verified. Precise leveling was conducted over the same period of time, in two campaigns. Nine vertical control points with known orthometric heights were used to fit a geoid model to a region of 20 km by 10 km. Orthometric heights were checked at other 17 points in the project area, resulting in a root mean square error of 2.2 cm. This accuracy compares favorably with the general standards specified for second-order (class II) leveling.