  In this paper, two tests, based on CUSUM of the residuals and least squares
estimation, are studied to detect in real time a change-point in a nonlinear
model. A first test statistic is proposed by extension of a method already used
in the literature but for the linear models. It is tested the null hypothesis,
at each sequential observation, that there is no change in the model against a
change presence. The asymptotic distribution of the test statistic under the
null hypothesis is given and its convergence in probability to infinity is
proved when a change occurs. These results will allow to build an asymptotic
critical region. Next, in order to decrease the type I error probability, a
bootstrapped critical value is proposed and a modified test is studied in a
similar way. Simulation results, using Monte-Carlo technique, for nonlinear
models which have numerous applications, investigate the properties of the two
statistic tests.
