  Most studies in real time change-point detection either focus on the linear
model or use the CUSUM method under classical assumptions on model errors. This
paper considers the sequential change-point detection in a nonlinear quantile
model. A test statistic based on the CUSUM of the quantile process subgradient
is proposed and studied. Under null hypothesis that the model does not change,
the asymptotic distribution of the test statistic is determined. Under
alternative hypothesis that at some unknown observation there is a change in
model, the proposed test statistic converges in probability to $\infty$. These
results allow to build the critical regions on open-end and on closed-end
procedures. Simulation results, using Monte Carlo technique, investigate the
performance of the test statistic, specially for heavy-tailed error
distributions. We also compare it with the classical CUSUM test statistic.
