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Current systems are very often based on large-scale, unpredictable and unreliable infrastructures. However, users of these systems increasingly require services with timeliness properties. This creates a difficult-to-solve contradiction with regard to the adequate time model: should it be synchronous, or asynchronous? In this paper, we propose an architectural construct and programming model which address this problem. We assume the existence of a component that is capable of executing timely functions, however asynchronous the rest of the system may be. We call this component the "timely computing base", and it can be used by the other components to execute a set of simple but crucial time-related services. We also show how to use it to build dependable and timely applications exhibiting varying degrees of timeliness assurance, under several synchrony models.