Wait-freedom and obstruction-freedom have received a lot of attention in the literature. These are symmetric progress conditions in the sense that they consider all processes as being “equal”. Wait-freedom has allowed to rank the synchronization power of objects in presence of process failures, while (the weaker) obstruction-freedom allows for simpler and more efficient object implementations. This paper introduces the notion of asymmetric progress conditions. Given an object O in a shared memory system of n processes, we say that O satisfies (y, x)-liveness if O can be accessed by a subset of y ≤ n processes only, and it guarantees wait-freedom for x processes and obstruction-freedom for the remaining y−x processes. Notice that, (n, n)-liveness is wait-freedom while (n, 0)-liveness is obstruction-freedom. The main contributions are: (1) an impossibility result showing that there is no (n, 1)-live consensus object even if one can use underlying (n − 1, n − 1)-live consens...