We describe the Timed Input/Output Automata (TIOA) framework, a general mathematical framework for modeling and analyzing real-time systems. It is based on timed I/O automata, which engage in both discrete transitions and continuous trajectories. The framework includes a notion of external behavior, and notions of composition and abstraction. We define safety and liveness properties for timed I/O automata, and a notion of receptiveness, and prove basic results about all of these notions. The TIOA framework is defined as a special case of the new Hybrid I/O Automata (HIOA) modeling framework for hybrid systems. Specifically, a TIOA is an HIOA with no external variables; thus, TIOAs communicate via shared discrete actions only, and do not interact continuously. This restriction is consistent with previous real-time system models, and gives rise to some simplifications in the theory (compared to HIOA). The resulting model is expressive enough to describe complex timing behavior, and to express the important ideas of previous timed automata frameworks.