Trapping‐detrapping pulse shapes have been observed in two Si(Li) detectors in the temperature range 8.5–70°K. A semiquantitative treatment leads to the conclusion that shallow trapping levels are responsible for the observed phenomena. It appears likely that these levels correspond to the donor (Li) and acceptor (B) dopants; if this hypothesis is confirmed by further experimental work it establishes a low‐temperature limit on the use of semiconductor detectors for &ggr;‐ray and high‐energy particle spectroscopy.