The Earth's magnetic field has been undergoing a remarkably systematic variation during the last 30 years. This variation can be described by a constant time derivative and a step-function second derivative. These parameters are smoothly distributed over the Earth's surface. The step occurred in 1969 and caused the second derivative to change signs for all of the components at most of the magnetic observatories. Similar but less well documented behaviour had been observed around 1900; it seemed to correlate with ajump in the acceleration of the Earth's rotation. We have investigated the motions at the top of the Earth's core that are responsible for the recent magnetic variations by inversion procedures. The motions responsible for the time derivative of the magnetic field can be reasonably well assessed ancl are dominated by a westward drift term of approximately 0.2 degrees /year, although important poloidal motions are also inferred. The data for the jump in the second derivative are much noisier and the motion accelerations are not as well resolved. The poloidal acceleration terms are still fairly well resolved, but the toroidal motions, especially the zonal motions, are very poorly resolved. No firm conclusion about an acceleration of the westward drift can be given on the basis of this analysis. The inversions give evidence that the motions for the lower modes are a strongly decreasing function of their order.