Using the horizontal components from El Centro 1940, Taft 1952, and 4 accelerograms from the San Fernando earthquake of 2/9/71, the time history of the elasto-plastic displacement response was calculated for oscillators having periods within the range of 1 to 6 s and ductility factors within the range of 3 to 6. The Nth largest peak of the elasto-plastic response (N equals 2,4,8,16), when expressed as a percentage of maximum response (that is, N equals 1), is fairly independent of period within our period range. When considering only plastic peaks occurring, sometimes in a one-directional group of peaks, in the reverse direction from the preceding plastic peak, the amplitude of the Nth reversing plastic peak is similar to the Nth elastic peak, regardless of the ductility factor.