Current approaches to model checking distributed systems reduce the problem to that of model checking centralized systems: global states involving all nodes and communication links are systematically explored. The frequent changes in the network element of the global states lead however to a rapid state explosion and make it impossible to model check any non-trivial distributed system. We explore in this paper an alternative: a local approach where the network is ignored, a priori: only the local nodes' states are explored and in a separate manner. The set of valid system states is a subset of all combinations of the node local states and checking validity of such a combination is only performed a posteriori, in case of a possible bug. This approach drastically reduces the number of transitions executed by the model checker. It takes for example the classic global approach several minutes to explore the interleaving of messages in the celebrated Paxos distributed protocol even considering only three nodes and a single proposal. Our local approach explores the entire system state in a few seconds. Our local approach does clearly not eliminate the state exponential explosion problem. Yet, it postpones its manifestations till some deeper levels. This is already good enough for online testing tools that restart the model checker periodically from the current live state of a running system. We show for instance how this approach enables us to find two bugs in variants of Paxos.