This paper discusses the static device operation of pmosts fabricated in high-resistivity (HR) Si substrates at cryogenic temperatures. It is shown that the anomalies observed at room temperature, i.e. the subthreshold leakage and the parasitic bulk conduction in saturation, are still present at 77 K and at 4.2 K, although considerable improvement of the subthreshold behaviour is observed. Furthermore, unlike mosts fabricated in standard substrates, little hysteresis is observed in the I-V characteristics down to liquid-helium temperatures. The observations are discussed in view of an analytical model adapted for HR-Si devices, which is extended for low-temperature operation. Finally, the effect of a reverse substrate bias, which is important for nuclear-radiation detection applications, and of the substrate contact on the device characteristics is demonstrated and discussed.