  The article studies the reiterated homogenization of linear elliptic
variational inequalities arising in problems with unilateral constrains. We
assume that the coefficients of the equations satisfy and abstract hypothesis
covering on each scale a large set of concrete deterministic behavior such as
the periodic, the almost periodic, the convergence at infinity. Using the
multi-scale convergence method, we derive a homogenization result whose limit
problem is of the same type as the problem with rapidly oscillating
coefficients.
