In distributed real-time systems it is often useful for a process p to know that another process q will not use a certain piece of information that p has sent to q beyond a certain deadline. If p can learn about the occurrence of the deadline by simply measuring the passage of time on its own local clock, we call this kind of information exchange `communication by time'. It is shown that communication by time is possible in systems where there exists no a priori known upper bound on the transmission delay of messages and where clocks are not synchronised. It is sufficient if one can compute an a posteriori upper bound on the transmission delay of a message m, i.e. at the time when m is delivered. The authors show how one can compute an a posteriori upper bound on the one-way message transmission delay of a message even if the clocks of the sender and receiver process are not synchronised. The method is used to design a fail-aware datagram service. This service supports communication by time by delivering all messages whose computed one-way transmission delays are smaller than a given bound as `fast' and all other messages as `slow'.The properties of this service are specified and an efficient implementation is provided for it. To illustrate how this service supports communication by time, a leader election protocol that guarantees the existence of at most one leader at any real time is sketched and it is shown how this allows the detection of out-of-date sensor information in process control applications.