Calorimetrically determined energy losses for a series of niobium and niobium‐25 at.% zirconium samples carrying an af transport current agreed with those calculated from hysteresis loops determined by dc magnetization measurements. The results of this study showed that the energy losses in ultra‐high‐purity annealed Nb are less than those for any of the other samples studied at magnetic fields less than 1500 G. The magnetic field dependence of the energy losses in all of the samples studied is given byEL=E12hm, whereELis the energy dissipated per unit surface area per cycle and is independent of frequency,E12is a constant which depends on the material and surface finish, andh=Hp/Hc1, whereHpis the peak ac field amplitude, andHc1is the lower critical magnetic field;m=n1whenh≤1, andm=n2whenh≥1. For both highly reversible and highly irreversible samples,n1≈ 3. For the least reversible samples,n2≈ 4, increasing to ∼8 for the most reversible samples studied.E12generally increased with decreasing reversibility and was strongly dependent on the surface finish of the sample, increasing as the surface roughness increased. The power lossPLper unit surface area is given byPL= (EL)f. This linear frequency dependence is consistent with a hysteretic loss mechanism as is the agreement between the calorimetrically determined losses and those calculated from the measured hysteresis loops.