In this paper we present an algorithm that can be used to implement sequential, causal, or cache consistency in distributed shared memory (DSM) systems. For this purpose it has a parameter that allows to choose the consistency model to be implemented. As far as we know, this is the first algorithm proposed that implements cache coherence.In our algorithm, when implementing causal and cache consistency all read and write operations are executed locally (i.e., are {fast}). It is known that no sequential algorithm has only fast memory operations. However, in our algorithm, when implementing sequential consistency all write operations and some read operations are fast.The algorithm uses propagation and full replication, where values written by a process are propagated to the rest of processes. It works in a cyclic turn fashion, with each process of the DSM system broadcasting one message in its turn. The values written by the process are sent in the message (instead of sending one message for each write operation), but unnecessary values are excluded. All this allows to control the amount of message traffic due to the algorithm.