  Attractiveness is a fundamental tool to study interacting particle systems
and the basic coupling construction is a usual route to prove this property, as
for instance in the simple exclusion process. We consider here general
exclusion processes where jump rates from an occupied site to an empty one
depend not only on the location of the jump but also possibly on the whole
configuration. These processes include in particular exclusion processes with
speed change introduced by F. Spitzer in [18]. For such processes we derive
necessary and sufficient conditions for attractiveness, through the
construction of a coupled process under which discrepancies do not increase. We
emphasize the fact that basic coupling is never attractive for this class of
processes, except in the case of simple exclusion, and that the coupled
processes presented here necessarily differ from it. We study various examples,
for which we determine the set of extremal translation invariant and invariant
probability measures.
