We consider systems consisting of finite automata communicating by exchanging messagesand working on the same read-only data.We investigate the situation in which the automata work with constantbut different speeds. We assume furthermore that the automata are not aware of the speeds andthey cannot measure them directly. Nevertheless, the automata have to compute a correct output. We call this model multi-speed systems of finite automata.Complexity measure that we consider here is the number of messages sent by the automata.The main result of this paper is that multi-speed systems are as powerful as synchronous systems, in whichall automata work with the same speed.