Mobile computing attracts more and more attention in recent years. Adaptive mobile computing systems need to process a broad range of composite events, which are combinations of primitive events such as logic event, time events, and temporal events, etc. This paper focuses on the design and implementation of composite events and composite actions in mobile computing systems, the sophisticated cases of event stream, time event and various operators are taken into consideration. Detection for composite events is supported efficiently by new kinds of extended automaton?Unidirectional Queue Automata and Bounded Unidirectional Queue Automata, which are defined and discussed in detail. The data structures and the mechanisms adopted by these new automata are described and how they can be efficiently applicable to adaptive mobile environments is illustrated.