The effects of time delay in the continuous part of a pulse-modulated model of non-basal endocrine feedback regulation are investigated. Conditions for the existence and local orbital stability of periodical solutions with m impulses in the least period (m-cycles) are derived. Applied to the case of testosterone regulation in the human male, the model indicates that increasing time delays in the system in hand typically lead to less complex dynamic pattern in the closed-loop system by giving rise to stable cycles of lower periodicity.