Based on a discussion of timed automata and a subset of these called PLC automata, described by H. Dierks, the problem of the composition of PLC automata is presented. Two methods for performing this composition are described, synchronous and asynchronous. The synchronous method requires that if and only if both initial automata accept a timed word, then it will appear in the resultant automaton. However, we prove that PLC automata are not closed under this form of composition. From this we introduce the asynchronous composition, which requires synchronization on the symbol element of the timed word alone. Four possible methods of asynchronous composition are described, and their effects on the 'essential' language, the language containing only words with no ignored symbols, are discussed. A few elementary results are also presented.