The kinematic history of the Rocky Mountain foreland and adjacent areas is computed back to 85 Ma, using virtually all the structural, paleomagnetic, and stress data in the literature. A continuous velocity field is fit to the data in each time step by weighted least squares, and this velocity is integrated back through time. As proposed by Hamilton <1981>, the net movement of the Colorado Plateau was a clockwise rotation about a pole in northern Texas; but the rotation was less (3¿) than some have inferred from paleomagnetism. The Laramide orogeny occurred during 75--35 Ma, with peak Colorado Plateau velocities of 1.5 mm yr-1 during 60--55 Ma. The mean azimuth of foreland velocity and mean direction of foreland shortening was stable at 40¿ for most of the orogeny, increasing to 55¿ in 50--40 Ma; the counter-clockwise rotation of shortening directions proposed by some previous authors is incorrect. Comparing the computed histories of foreland flow speed and direction with the known motions of the Kula and Farallon plates confirms that the Laramide orogeny had a different mechanism from the early Sevier orogeny: it was driven by basal traction during an interval of horizontal subduction, not by edge forces due to coastal subduction or the spreading of the western cordillera or by accretion of terranes to the coast. Tentatively, a minor clockwise rotation of shortening directions at 50 Ma may record the passage of an active Kula-Farallon transform within the subducted slab. ¿ 1998 American Geophysical Union