The geodetic results of Ma et al. <1994> from very long baseline interferometry are used to assess rates of intraplate deformation. We analyze the resulting set of velocities of 18 plate-interior sites, nine on the North American plate, four western European sites on the Eurasian plate, three on the Pacific plate, and two on the Australian plate. We formulate three alternative error budgets based partly on the work of Ryan et al. <1993a>: an optimistic error budget, a conservative error budget, and an upper bound error budget. All three budgets assume the existence of a previously unmodeled error that is inversely proportional to the time span of observations at a site. Use of the conservative error budget indicates no significant motion between sites on any one of the four plates. Use of the upper bound error budget, designed to be precisely large enough to be consistent with rigid plates, places a usefully small upper bound on how fast any site might be moving relative to the rest of its plate. Speeds faster than 2 mm/yr are excluded at the 95% confidence level for seven of the 18 plate-interior sites. Adjustments of the site velocities for motion due to postglacial rebound as predicted from the model of Tushingham and Peltier <1991> give an insignificant improvement to the fit of the horizontal velocities to the rigid plate model. The velocities of six sites near the western margin of the interior of the North American plate were also analyzed. Use of the conservative error budget indicates that a site near Fairbanks (Alaska) has an upper bound of 3 mm/yr on its speed, a site in Nome (Alaska) has an upper bound on its speed of ~8 mm/yr, and a site in Penticton (British Columbia) has an upper bound on its speed of ~4 mm/yr. Of three sites on the Colorado Plateau, two move marginally significantly, and one moves insignificantly relative to stable North America. Upper limits on their speeds relative to stable North America range from 4 to ~5 mm/yr. We conclude that the data do not yet demonstrate significant velocities between sites in the stable interior of any one plate but do provide useful and small upper bounds of 2 mm/yr or less on the speeds of the best observed intraplate sites. Six sites near the western margin of the North American interior have upper bound speeds of 3 to 8 mm/yr. ¿ American Geophysical Union 1996