Finite State Machines (FSMs) are widely used for analysis and synthesis of digital components of control systems. In order to take into account time aspects, timed FSMs are considered. In this paper, we address the problem of deriving a parallel composition of FSMs with timed guards and output delays (output timeouts). When the parallel composition is considered, component FSMs work in the dialog mode and the composition produces an external output when the interaction between components is terminated. We formally define the parallel composition operator for FSMs with timed guards (TFSMs) and show that unlike classical FSMs, a "slow environment" is not sufficient for describing the behavior of a composition of deterministic TFSMs by a deterministic FSM with a single clock. Although the set of deterministic FSMs with timed guards is not closed under the parallel composition operator, some classes of deterministic TFSMs are still closed under this operator and the paper contains some examples of such classes.