We are interested here in the reachability and controllability problems for DEDS in the max-algebra. We show that these problems lead to an eigenvector problem in the min algebra. More precisely, we show that, given a max-linear system, then, for every natural number , there is a matrix whose eigenspace associated with the eigenvalue 1 (the multiplicative identity, which coincides here with the real number 0) in the min algebra contains all the states which are reachable in k steps. This means in particular that if a state is not in this eigenspace, then it is not controllable. A similar result also holds by duality on the observability side.