High-resolution OH 1612-MHz spectra are presented of the supergiant OH-IR sources VY CMa, VX Sgr, IRC 10420 and NML Cyg. The spectra have a resolution of 300 Hz. Narrow components in the spectra have linewidths as small as 550 Hz (0.1 km s-1) but there is no evidence for components narrower than this. These results are in accord with present understanding of maser line-narrowing and of the physical conditions in the OH maser regions. Many of the narrow components have an appreciable degree of circular polarization which is not apparent at the lower frequency resolutions usually employed. The circular polarization indicates the presence of magnetic fields of approximately 1 mG in the circumstellar envelopes, at distances of approximately 3x10(16) cm from the central stars. These fields are strong enough to influence the outflow from the stars, and may help to explain some of the asymmetries which are seen in their circumstellar envelopes.