We present recent measurements of the top quark mass using events collected at the CDF and D0 detectors from pp-bar collisions at s**(1/2) = 1.96 TeV at the Fermilab Tevatron. These analyses are performed using events consistent with the decay channel tt-bar --> b-bar l- nu-bar_l' + nu'_l, or the dilepton channel, 230-360 pb-1 of data are used.