  We construct a zero-entropy weakly mixing finite-valued process with the
exponential limit law for return resp. hitting times. This limit law is
obtained in almost every point, taking the limit along the full sequence of
cylinders around the point. Till now, the exponential limit law for return
resp. hitting times, taking the limit along the full sequence of cylinders,
have been obtained only in positive-entropy processes satisfying some strong
mixing conditions of Rossenblatt type.
