We have used very long baseline interferometry observations from the International Radio Interferometric Surveying and Crustal Dynamics Project programs taken over a time span of 5--8 years (through August 1990) to derive relative velocities of 16 sites on the North American, Eurasian, Pacific, and African plates. The data reduction scheme simultaneously estimates Earth orientation parameters and nutation for each session, local atmosphere and clock correction terms, source positions, and initial site positions, as well as the site velocities. No a priori geophysical crustal model whatsoever is imposed to obtain the velocities. Instead we introduce a minimal set of geometric constraints to obtain the solution. Two alternative constraint formulations are considered; they are shown to be equivalent in that they yield equivalent velocity sets with allowance for translation and rotation. These are (1) setting the secular motion of the pole and mean length of day to fixed values and (2) fixing the net rotation of the sites. The resulting velocities have formal standard errors typically <0.2 cm/yr, and most velocities are significantly different from zero. They agree closely to within 0.5 cm/yr, with velocities predicted by the Minster-Jordan and NUVEL-1 plate motion models, after allowing for the arbitrary rotation and translation between the systems. The velocity of Kashima, Japan, is much more consistent with the North American plate than the Eurasian plate where current plate model boundaries place it. We suggest another possibility: Kashima does lie on the Eurasia plate, but its motion is so modified by interaction with the nearby Pacific plate as to result in the observed velocity. Sites near the active plate boundary in California also show motions intermediate between those of the adjoining plates. ¿ American Geophysical Union 1992