Surface and body wave magnitudes are determined for 15 U.S.S.R. underground nuclear weapons tests conducted at Novaya Zemlya between 1964 and 1976 and are used to estimate yields. These events include the largest underground explosions detonated by the Soviet Union. A histogram of body wave magnitude (m(b)) values indicates a clustering of explosions at a few specific yields. The most pronounced cluster consists of six explosions of yield near 500 kilotons. Several of these seem to be tests of warheads for major strategic systems that became operational in the late 1970s. The largest Soviet underground explosion is estimated to have a yield of 3500 +/- 600 kilotons, somewhat smaller than the yield of the largest U.S. underground test. A preliminary estimation of the significance of tectonic release is made by measuring the amplitude of Love waves. The bias in m(b) for Novaya Zemlya relative to the Nevada test site is about 0.35, nearly identical to that of the eastern Kazakhstan test site relative to Nevada.