The paper presents a primary-backup protocol to manage replicated in-memory database systems (IMDBs). The protocol exploits two features of IMDBs: coarse-grain concurrency control and deferred disk writes. Primary crashes are quickly detected by backups and a new primary is elected whenever the current one is suspected to have failed. False failure suspicions are tolerated and never lead to incorrect behavior. The protocol uses a consensus-like algorithm tailor-made for our replication environment. Under normal circumstances (i.e., no failures or false suspicions), transactions can be committed after two communication steps, as seen by the applications. Performance experiments have shown that the protocol has very low overhead and scales linearly with the number of replicas.