In previous papers, we have presented both a new framework for building flexible hard real-time systems (FRTS) and a corresponding run-time support system, called Flexible Real-Time Linux (FRTL). This paper presents how timing exception support can be integrated in both the framework and the run-time system. In particular, the paper proposes detecting and handling two types of timing exceptions: tasks overrunning their worst-case execution times (wcets) and tasks missing their deadlines. This paper shows that the support for these two types of exceptions is required in order to deal with excessive CPU consumption of the application tasks and the kernel itself, respectively. The handling mechanism for wcet exceptions incorporates the possibility of attaching a user-defined handler to each application task. Handlers are defined to be scheduled as either mandatory or optional components at any priority. The specific overhead related to all these mechanisms has been incorporated into the system's complete feasibility test, which is also presented.