The mechanisms governing the upconversion fluorescence from the 1G4 level of Tm3+ ions have been investigated in fluorozirconate glass doped with Tm3+ only and codoped with Tm3+ and Yb3+ ions, under 649 (H-3(4) --> 1G4) and 684 nm (H-3(6) --> F-3(3)) excitation wavelengths. The emission intensity depends on the excitation power quadratically in both samples, showing the two-photon absorption nature of the processes. An enhancement of the 1G4 --> H-3(6) emission was observed in the codoped sample under 684 nm excitation. The upconversion emission in the single doped sample is mainly due to the E.S.A. process upon both excitations. The dominant mechanism was found to be the energy transfer process between Tm3+ and Yb3+ ions in the codoped sample when the excitation was tuned at 684 nm. The upconverted emission intensity shows a different temperature dependence under the two excitations in the codoped sample. However, for the 649 nm excitation the dependence is the same in both samples. This confirms the dominance of the E.S.A. process under 649 nm excitation in both, singly and doubly doped samples.