The correct and efficient implementation of general real-time applications remains very much an open problem. A key issue is meeting timing constraints whose satisfaction depends on features of the execution platform, in particular its speed. Existing rigorous implementation techniques are applicable to specific classes of systems, for example, with periodic tasks or time-deterministic systems. We present a general model-based implementation method for real-time systems based on the use of two models: 1) An abstract model representing the behaviour of real-time software as a timed automaton, which describes user-defined platform-independent timing constraints. Its transitions are timeless and correspond to the execution of statements of the real-time software. 2) A physical model representing the behaviour of the real-time software running on a given platform. It is obtained by assigning execution times to the transitions of the abstract model. A necessary condition for implementability is time-safety, that is, any (timed) execution sequence of the physical model is also an execution sequence of the abstract model. Time-safety simply means that the platform is fast enough to meet the timing requirements. As execution times of actions are not known exactly, time-safety is checked for the worst-case execution times of actions by making an assumption of time-robustness: time-safety is preserved when the speed of the execution platform increases. We show that, as a rule, physical models are not time-robust, and that time-determinism is a sufficient condition for time-robustness. For a given piece of real-time software and an execution platform corresponding to a time-robust model, we define an execution engine that coordinates the execution of the application software so that it meets its timing constraints. Furthermore, in the case of non-robustness, the execution engine can detect violations of time-safety and stop execution. We have implemented the execution engine for BIP programs with real-time constraints and validated the implementation method for two case studies. The experimental results for a module of a robotic application show that the CPU utilisation and the size of the model are reduced compared with existing implementations. The experimental results for an adaptive video encoder also show that a lack of time-robustness may seriously degrade the performance for increasing platform execution speed.