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.
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