  We present circular polarization measurements of circumstellar water masers
around 2 Mira variables and 4 supergaint stars. Both an LTE and non-LTE method
are used to analyze the circular polarization and total intensity spectra and
to obtain the magnetic field strength. The non-LTE method is found to be able
to reproduce the observations best. Using this, we find fields from a few
hundred milliGauss up to a few Gauss, indicating a solar-type r^(-2) dependence
of the magnetic field on the distance, which leads to stellar surface magnetic
fields of up to several hundred Gauss. No linear polarization is detected to
less than 1.5%.
