Many workers have encountered difficulties with determination of the absolute motion of the Eurasian plate. The problem is accident of vector geometry caused by addition by two angular velocity vectors about 180° from each other and of similar length. Twp-proposed systems of absolute motion yield Eurasian plate motions at right angles to each other while the motions of most other plates vary little from system to system. The phenomenon is associated with slow-moving plates. To resolve this problem, much more precise relative and absolute motion idata will be needed. This kind of geometrical Accident could affect both relative and absolute plate reconstructions as they are extended back in time and might explain some of the apparent motion between hot spots suggested by other workers.