It is thought that small 'static' stress changes due to permanent fault displacement can alter the likelihood of, or trigger, earthquakes on nearby faults. Many studies of triggering in the nearfield, particularly of aftershocks, rely on these static changes as the triggering agent and consider them only in terms of equivalent changes in the applied load on the fault. Here we report a comparison of the aftershock pattern of the moment magnitude MW = 7.3 Landers earthquake, not only with static stress changes but also with transient, oscillatory stress changes transmitted as seismic waves (that is, 'dynamic' stresses). Dynamic stresses do not permanently change the applied load and thus can trigger earthquakes only by altering the mechanical state or properties of the fault zone. These dynamically weakened faults may fail after the seismic waves have passed by, and might even cause earthquakes that would not otherwise have occurred. We find similar asymmetries in the aftershock and dynamic stress patterns, the latter being due to rupture propagation, whereas the static stress changes lack this asymmetry. Previous studies have shown that dynamic stresses can promote failure at remote distances, but here we show that they can also do so nearby.