The carrier concentration of Tl 2 Ba 2 CaCu 2 O 8 films was modified by annealing in N 2 gas. X-ray analysis of the structure and the oxygen content revealed a correspondence between carrier concentration and oxygen depletion. The T C and nonlinear surface impedance was measured using a dielectric resonator and the nonlinearity slope parameter r=X S /R S was found to converge to unity at the critical temperature, indicating a dominance of Josephson fluxon hysteresis on the nonlinearity. Highly inductive nonlinearity was observed in a small range of doping levels between 0.180