We evaluate a new method of Global Positioning System (GPS) data analysis, called instantaneous positioning, at spatial scale lengths typical of interstation spacings in a modern crustal motion network. This method is more precise and versatile than traditional GPS static and kinematic processing of multi-epoch batches of data. The key to instantaneous positioning is the ability to resolve integer-cycle phase ambiguities with only a single epoch of dual-frequency phase and pseudorange data, rendering receiver cycle slips irrelevant. We estimate three-dimensional relative coordinates and atmospheric zenith delay parameters independently every 30 s over a 12-week period for baseline distances of 50 m, 14 km, and 37 km. Horizontal precision of a single-epoch coordinate solution is about 15 mm and vertical precision is about 7--8 times worse. Removing that component of each time series which repeats with a period of exactly 1 sidereal day, and thus manifests signal multipath, reduces the scatter by about 50% in all components. Solution averaging of the high-frequency time series can be performed using any number of measurement epochs to further improve coordinate precision. We demonstrate that the daily coordinates estimated with instantaneous positioning are more precise (by 20--50% per coordinate component) than those estimated with 24-hour batch processing. Spectral analysis of the single-epoch solutions indicates that the flicker noise characteristic of GPS time series observed in lower-frequency bands also affects GPS solutions in the frequency band 0.01 mHz to 10 mHz. We argue that the flicker noise is induced by tropospheric effects. Since modern GPS receivers are capable of observing at frequencies as high as 10 Hz, our technique significantly overlaps and complements the frequency band of broadband seismology and benefits other research areas such as earthquake geodesy, volcanology, and GPS meteorology. ¿ 2000 American Geophysical Union