The neutron spectra of an 80 g PuBe source and an 11 Ci PoBe source were measured by differentiation of proton track distributions sampled from nuclear emulsion. Special analysis of the track distributions revealed peaks at 0.54, 0.78, 1.1, 2.3, 3.2, 4.8, 5.6, 7.8 and 9.8 MeV in both spectra. The common features and the differences in the two sources are interpreted by use of a numerical graphical analysis based on published differential and integral cross sections for the 9Be(α,n) reaction. In contrast to earlier theoretical and semiempirical attempts, this analysis successfully explains the major features of various measured 9Be(α,n) source neutron spectra. Partial-wave (resonance) theory predictions of the reaction anisotropy of the neutron groups in such spectra are made and discussed.