This paper deals with the asymptotic properties
of quasi-maximum likelihood estimators for multivariate
heteroskedastic models. For a general model, we give conditions
under which strong consistency can be obtained; unlike
in the current literature, the assumptions on the existence
of moments of the error term are weak, and no study of
the various derivatives of the likelihood is required.
Then, for a particular model, the multivariate GARCH model
with constant correlation, we describe the set of parameters
where these conditions hold.