Real-time programs are, in general, difficult to design and verify. The inheritance mechanism can be useful in reusing well-defined and verified real-time programs. In applications developed by current real-time objectoriented languages, however, changing application requirements or changing real-time specifications in subclasses may require excessive redefinitions although this seems to be intuitively unnecessary. We refer to this as the real-time specification inheritance anomaly. This paper introduces three kinds of real-time specification inheritance anomalies that one may experience while constructing object-oriented programs. As a solution to these anomalies, the concept of real-time composition filters is introduced. Filters affect the real-time characteristics of messages that are received or sent by an object. Through proper configuration of filters, one can specify real-time constraints, and reuse of these constraints without causing inheritance anomalies.