Presents a computational framework based on tabled resolution and constraint processing for verifying real-time systems. We also discuss the implementation of this framework in the context of the XMC/RT (eXtended Model Checker/Real-Time) verification tool. For systems specified using timed automata, XMC/RT offers backward and forward reachability analysis, as well as timed modal mu-calculus model checking. It can also handle timed infinite-state systems, such as those with unbounded message buffers, provided the set of reachable states is finite. We illustrate this capability on a real-time version of the Leader Election protocol. Finally, XMC/RT can function as a model checker for untimed systems. Despite this versatility, preliminary benchmarking experiments indicate that XMC/RT's performance remains competitive with that of other real-time verification tools.