Agreement problems allow a set of processes to agree on a common output value. These problems are of primary importance in distributed systems and difficult to solve in presence of failures. This paper considers one of these problems whose practical interest is well known, namely the Non-Blocking Atomic Commitment Problem. First, a generic protocol solving this problem is given and then instantiations of its generic statements are provided for both synchronous and asynchronous distributed systems. These instantiations use timeout mechanism, reliable multicast primitives and unreliable failure detectors as basic components. Incidentally, this paper can also be considered as an introduction to state-of-the-art concepts and mechanisms of distributed fault tolerance.