The electron paramagnetic resonance spectra of multicomponent fluoride glasses in the system AlF3-YF3-Sigma RF(2) (R = Ba, Ca, Sr, Mg) have been measured after gamma-ray irradiation at 77 K. The samples of nominal compositions Ba(2)EMgAl(2)F(14) (E = Sr, Ca, Pb) and BaYRMgAl(2)F(15) (R = Ba, Sr, Ca, Zn, Cd, Pb) were investigated in the same manner for comparison purposes. The hole center, F-2(-), has been identified in these materials. An electron center with g(parallel to) = 1.995 +/- 0.005 and g(perpendicular to) = 1.93 +/- 0.01 has been attributed to a Y2+ ion which can be considered as a Y3+ ion that has trapped an electron on its d-orbital. This center annealed out between 110 and 120 K. The symmetric single line with g = 2.015 +/- 0.002 and linewidths varing from 4.5 to 7.5 mT for different samples has been observed in a wide range of temperatures (from 77 to 520 K). It is assumed that this line is the superposition of two hole signals: one of them is a hole trapped on several fluorine ions and the other is a hole trapped on an oxygen impurity. The high oxygen content, which is confirmed by X-ray photoelectron spectroscopy measurements, leads to a broadening of the line attributed to oxygen impurity.