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The distributed delay has found widespread application in the modeling of aggregative processes involving the flow of entities with random transit times through a given process. In most of these applications it is assumed that the mean entity transit time is fixed. There are, however, a number of important applications in aggregative economic, physical, social, and biological systems in which the mean entity transit time is time varying. A time-varying distributed delay model is developed along with a Fortran subroutine for its simulation as part of a larger system model. Examples illustrate applications of this time-varying distributed delay model to aggregative biological and economic processes.