Abstract: A self-stabilizing algorithm, regardless of the initial system state, converges in finite time to a set of states that satisfy a legitimacy predicate without the need for explicit exception handler of backward recovery. The l-mutual exclusion is a generalization of the fundamental problem of mutual exclusion: the system has to guarantee the fair sharing of a resource that can be used by l processors simultaneously. We present a space efficient solution to the l-mutual exclusion problem that performs on uniform unidirectional ring networks and that is self-stabilizing. Our solution improves the space complexity of previously known approaches by a factor of \min(n^2\times \log(n), 1\over l\times \log^{l-1}(n)), while retaining none of their drawbacks in terms of system hypothesis (we support unfair scheduler and ensure strong correctness) or specification verification (we guarantee high level l-mutual exclusion). When l is fixed, the space complexity at each node is constant in average, making our approach suitable for scalable systems. Extensive proofs can be found in [15].