This paper presents a new computational model for realtime systems, called the clocked transition system (CTS) model The CTS model is a development of our previous timed transition model, where some of the changes are inspired by the model of timed automata. The new model leads to a simpler style of temporal specification and verification~ requiring no extension of the temporal language. We present verification rules for proving safety properties (including time-bounded response properties) of clocked transition systems, and separate rules for proving (time-unbounded) response properties. All rules are associated with verification diagrams. The verification of response properties requires adjustments of the proof rules developed for untimed systems, reflecting the fact that progress in the reM time systems is ensured by the progress of time and not by fairness. The style of the verification rules is very close to the verification style of untimed systems which allows the (re)use of verification methods and tools, developed for untimed reactive systems for proving all interesting properties of real-time systems. We conclude with the presentation of a branching-time based approach for verifying that an arbitrary given CTS is non-zeno. Finally, we present an extension of the model and the invariance proof rule for hybrid systems.