  Consider a symmetrical conflict relationship between the points of a point
process. The Mat\'ern type constructions provide a generic way of selecting a
subset of this point process which is conflict-free. The simplest one consists
in keeping only conflict-free points. There is however a wide class of Mat\'ern
type processes based on more elaborate selection rules and providing larger
sets of selected points. The general idea being that if a point is discarded
because of a given conflict, there is no need to discard other points with
which it is also in conflict. The ultimate selection rule within this class is
the so called Random Sequential Adsorption, where the cardinality of the
sequence of conflicts allowing one to decide whether a given point is selected
is not bounded. The present paper provides a sufficient condition on the span
of the conflict relationship under which all the above point processes are well
defined when the initial point process is Poisson. It then establishes, still
in the Poisson case, a set of differential equations satisfied by the
probability generating functionals of these Mat\'ern type point processes.
Integral equations are also given for the Palm distributions.
