We consider the theoretical and the practical aspects of using radiointerferometric observations of the Global Positioning System (GPS) satellites to establish a three-dimensional, multistation, geodetic control network. We discuss various ways of processing GPS data and try them with observations from a 35-station network in Germany. We examine the reproducibility of interferometric determination of individual baseline vectors and the three-dimensional vector closure of subnetworks and the whole network. We compare these measures of precision with corresponding predictions based on statistics of interferometric phase residuals. We conclude that the relative positions of stations in the network were determined by GPS interferometry within about 1 part per million (ppm) in both horizontal coordinates and about 1.6 ppm in the vertical. As an external test of horizontal accuracy, we compare baseline lengths with electro-optical distance measurements. The vertical accuracy is tested against determinations, by means of spirit leveling and gravimetry, of the height differences between stations. The differences between the interferometric and the independent determinations are consistent with the uncertainties of the latter. Interferometry with GPS is by far the most efficient method of establishing geodetic control on local and regional scales. This is already true, even though the constellation of satellites is incomplete. The accuracy of regional control by GPS should improve to about 0.1 ppm when interferometry is also used to determine the satellite orbits.