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Formal models used for representing recurrent real-time processes have traditionally been characterized with a period parameter that specifies the minimum amount of time that may elapse between successive invocations of the process. However a recently proposed model called the non-cyclic GMF model has the distinctive feature that there need be no single period parameter characterizing the recurrent behavior of the task. This paper studies the implications of removing the restriction of requiring a unique period parameter to other previously-proposed models for representing recurrent processes. It is shown that removing this restriction represents a significant generalization to these prior models. Despite the added generality, however, feasibility analysis on preemptive uniprocessors remains tractable.