  We observed 14 methanol transitions near lambda=2 mm in Galactic star-forming
regions. Broad, quasi-thermal J(0)-J(-1)E methanol lines near 157 GHz were
detected toward 73 sources. Together with the 6(-1)-5(0)E and 5(-2)-6(-1)E
lines at 133 GHz and the 7(1)-7(0)E line at 165 GHz, they were used to study
the methanol excitation. In the majority of the observed objects, the Class I
6(-1)-5(0)E transition is inverted, and the Class II 5(-2)-6(-1)E and
6(0)-6(-1)E transitions are overcooled. This is exactly as predicted by models
of low gain Class I masers. The absence of the inversion of Class II
transitions 5(-2)-6(-1)E and 6(0)-6(-1)E means that quasi-thermal methanol
emission in all objects arises in areas without a strong radiation field, which
is required for the inversion.
