  There are many formalisms to describe quantum decoherence. However, many of
them give a non general and ad hoc definition of "pointer basis" or "moving
preferred basis", and this fact is a problem for the decoherence program. In
this paper we will consider quantum systems under a general theoretical
framework for decoherence and present a very general definition of the moving
preferred basis. In addition, this definition is implemented in a well known
model and the time of decoherence and the relaxation time are defined and
compared with those of this model.
