To assess the capability of Global Positioning System (GPS) phase measurements for the determination of transient velocity, we have made measurements with a GPS antenna on a moving platform. The antenna was translated in the horizontal plane at a constant velocity of 1 mm h-1 for a period of somewhat more than 24 hours while GPS data were recorded simultaneously. Other stationary antennas at distances of 10 m to ~1000 km were also simultaneously recording GPS data. We calculated an average velocity of the moving antenna by modeling its time-dependent position as a random walk and fitting a straight line to the stochastic estimates. We have found that the accuracy of the resulting velocity estimates is dependent on the observing period and the baseline length. For 24-hour data time spans, rms horizontal velocity errors were less than 0.2 mm h-1 for all baseline lengths; for similar time spans, rms vertical velocity errors were 0.3--0.9 mm for lengths between 100 and 1000 km, and ≲0.2 mm for baselines ≤1000 m. We found it convenient to define a quantity &xgr;, which we term the dynamic resolution, equal to the ratio of the rms velocity variation to the mean velocity. For a random walk process, &xgr;rw can be used to calculate the variance per unit time &sgr;2rw required by filter-based analysis software. We also investigated the power spectral density (PSD) of our estimates of time-dependent position and found that for the frequency range sampled (0.07--16 mHz), the PSD could be well modeled by &ngr;α, where &ngr; is the frequency and the spectral index α depends on the value of &xgr;. For strongly constrained (yet unbiased) estimates (obtained by choosing &xgr;rw=10 and &sgr;rw=0.05 mm h-1/2), the resultant value for α is -4, indicating a strong filtering of high-frequency noise. ¿ American Geophysical Union 1996