We present two distributed algorithms for dynamic replication of a data-item in communication networks. The algorithms are adaptive in the sense that they change the replication scheme of the item (i.e. the set of processors at which the data-item is replicated), as the read-write pattern of the processors in the network changes. Each algorithm continuously moves the replication scheme towards an optimal one, where optimality is defined with respect to different objective functions. One algorithm optimizes the communication cost objective function, and the other optimizes the communication time. We also provide a lower bound on the performance of any dynamic replication algorithm.