The specific heats of single crystals of NpTe and PuTe have been measured in the ranges 1.5-36 K and 5-9.5 K respectively, in a calorimeter designed for small samples. These measurements are the first at sufficiently low temperatures to allow a firm determination of each material's electronic contribution, gamma-T, to its specific heat. Both of these materials were found to be quite metallic in nature, with the gamma (in mJ mol-1 K-2) for PuTe equal to 30 +/- 5 and that for NpTe being 130 +/- 10. These data are compared with previous results from other measurements and the implications for understanding the electronic nature of plutonium in PuTe are discussed.