The dependence of thermoluminescence (TL) on the excitation dose was found in some cases to be superlinear. In particular, the peak at 100 oC in an unannealed synthetic quartz showed quadratic and super-quadratic behaviour. This strong superlinearity was explained by the possibility that electrons released during the heating phase may recombine with trapped holes yielding TL, get retrapped or get trapped in a competing state. The strong superlinearity was shown in a previous theoretical study to occur, using approximations such as small retrapping and small rate of change of free electrons concentration. In another theoretical work, superlinearity of the filling of traps was found by assuming a competition during the excitation phase. In the present work the solution of the excitation equations has been carried out first. The relaxation of excited carriers at a constant temperature was then simulated, and using the results as initial values for the competition during heating stage, the solution of the equations has been run. The final results of superlinearity thus obtained are discussed.