  The carrier concentration of Tl2Ba2CaCu2O8 films was modified by annealing in
N2 gas. X-ray analysis of the structure and the oxygen content revealed a
correspondence between carrier concentration and oxygen depletion. The TC and
nonlinear surface impedance was measured using a dielectric resonator and the
nonlinearity slope parameter r=dXS/dRS 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<p<0.195 holes/Cu, which does not include the
optimal doping level of 0.16 holes/Cu.
