The valence bands of HfxTi1-xSe2 have been studied by angle-resolved photoelectron spectroscopy for x=0.3 and 0.5. These results indicate the existence of small band gaps between valence and conduction bands in both these alloys. The authors interpret existing Hall effect data, which show evidence for high-mobility holes for the Hf0.3TiO.7Se2 sample, in terms of thermal excitations across the small band gap at high temperatures. They model the temperature and pressure dependence quantitatively, and determine the band gap of Hf0.3Ti0.7Se2 to be 104 meV at atmospheric pressure with a pressure derivative of -6 meV kbar-1. The new model is relevant also to TiSe2, but the conclusion that this material is semi-metallic in its high-temperature phase is unaffected.