The dynamics of discrete mechanical systems with perfect unilateral constra
ints is formulated in a very general setting. We study the resulting evolut
ion problem. The existence and uniqueness of a maximal solution is proved u
nder the hypothesis that the data are analytic. We also provide a sufficien
t condition to ensure that the maximal solution is defined for all rime. (C
) 1999 Academie des sciences/Editions scientifiques et medicales Elsevier S
AS.