Interrupt Timed Automata (ITA) have been introduced to model multi-task systems with interruptions. They form a subclass of stopwatch automata, where the real valued variables (with rate 0 or 1) are organized along priority levels. While reachability is undecidable with usual stopwatches, the problem was proved decidable for ITA. In this work, after giving answers to some questions left open about expressiveness, closure, and complexity for ITA, our main purpose is to investigate the verification of real time properties over ITA. While we prove that model checking a variant of the timed logic TCTL is undecidable, we nevertheless give model checking procedures for two relevant fragments of this logic: one where formulas contain only model clocks and another one where formulas have a single external clock.