The third-order nonlinearity is measured for TeO2-ZnO-Na2O (TZN) glasses codoped with BaO, Nb2O5, and La2O3. The results for the sign and magnitude of the nonlinearity were obtained using a combination of the eclipse Z-scan with thermal nonlinearity managed Z-scan, whereas the Kerr shutter technique was employed to obtain the electronic time response of the nonlinearity, all performed with 76 MHz repetition rate 150 fs pulses at 800 nm. The results show a fast response (< 200 fs) and a nonlinear refractive index varying from 1.5 to 3.5x10(-15) cm(2)/W, depending upon glass composition. At the peak power level employed, nonlinear absorption was negligible. The results obtained are in good agreement with other tellurite compositions reported, confirming the electronic origin of the nonlinearity.