  This paper considers M-estimation of a nonlinear regression model with
multiple change-points occuring at unknown times. The multi-phase random design
regression model, discontinuous in each change-point, have an arbitrary error
$\epsilon$. In the case when the number of jumps is known, the M-estimator of
locations of breaks and of regression parameters are studied. These estimators
are consistent and the distribution of the regression parameter estimators is
Gaussian. The estimator of each change-point converges, with the rate $n^{-1}$,
to the smallest minimizer of the independent compound Poisson processes. The
results are valid for a large class of error distributions.
