Third-order nonlinear susceptibilities χ(3)(−2ω;ω,ω,0) and χ(3)(−ω;ω,-ω,ω) responsible for electric-field-induced second harmonic generation and the optical Kerr effect were measured and directly compared for tellurite and chalcogenide glasses. The nonlinear coefficients were found by measuring the second harmonic radiation from samples under the action of an external field of terahertz pulses and by the classical z-scan technique, respectively. The influence of ambient air and helium gas on second harmonic generation was analyzed. It was demonstrated that both susceptibilities χ(3)(−2ω;ω,ω,0) and χ(3)(−ω;ω,-ω,ω) have close absolute values, which shows the dominant role of nonresonant electronic nonlinearity in the studied glasses.