The glass-forming regions in the MgSO4-Na2B4O7-K2SO4 and MgSO4-Na2B4O7-KHSO4 systems are shown to lie in the borate-rich corner of the composition triangle and to occupy about 20% of its area. IR and Raman spectroscopy results are used to develop a structural model of the glasses studied. Vibrational spectra suggest that the structure of the glasses is governed by borate glass-forming groups, which incorporate SO4 tetrahedra.