The study of the volatility, present in some time series, provoked the
appearance of models with autoregressive conditional heteroscedastici
ty, called ARCH (ENGLE (1982)). In order to account for asymmetries in
the volatility, RABEMANANJARA & ZAKOIAN (1992) introduced a new formu
lation for the conditional variance expressing it as a piecewise linea
r function of past values of the process as well as of past values of
the conditional variance itself. The aim of this paper is to study the
strong stationarity and the ergodicity of this kind of models, called
GTARCH. As a consequence, we obtain, for some concrete models, region
s of stationarity for their coefficients.