Energy distributions of fast secondary electrons ejected from Cu and Si bombarded by positrons of energies in the range 50 to 2000 eV, incident at glancing angles ͑#5 ± ͒ and at 35 ± , have been fit to the form AE 2m proposed by E. N. Sickafus. The absence of electron backscattering and the reduction of cascade effects common in electron-stimulated secondary electron spectra allow the direct determination of m for comparison with theory. The values obtained rise from 1.5 at 2000 eV to about 2.5 at 50 eV, and are all higher than those found for electrons incident at higher energies (0.5 -1.5). No significant dependence of the value of m on target species or angle of incidence was observed. [S0031-9007(97)03544-8] PACS numbers: 79.20.Hx