A calorimetric technique, involving measurement of the thermal conductivity, was used to measure non‐Ohmic ac power losses in short, 0.25‐mm‐diam samples of superconducting Nb‐25% Zr and Nb‐33% Zr wire as a function of frequency, current amplitude and waveform, and temperature. The observed power losses at 4.2°K ranged from 6×10−11to 10−7W/cm. The losses depended linearly on frequency in the range 60–40 000 cps and decreased approximately asT2.5for temperaturesTin the range 2.0°–4.2°K. Peak currents from 1 to 8 A were used to determine that the power loss was a function of the peak currentImrather than the rms current and also was proportional toImn, wherenvaried from 2.6 to 4.5. These results indicate a hysteresis loss mechanism with no detectable relaxation effects for the entire frequency range covered. Models which have been proposed to account for hysteresis losses in hard superconductors are discussed. The results of this experiment are compared with earlier measurements on Nb‐Zr alloys. There is considerable disagreement between the present results and the published results of Zar in magnitude and in the frequency and current dependences of the ac power losses.