Practically all of the studies of glycolytic oscillations in homogeneous spatial mediums have been performed through the construction of systems of ordinary differential equations and the search for their solutions. In this kind of modelling, the system dynamic behavior is considered to depend only on the values adopted by the parameters related to the dependent variables. In the present work, the modeling of a biochemical system through a system of functional differential equations with delay allows us to analyse the consequences that the variations in the parametric values linked to the independent variable (time) have upon the integral solutions of the system. In our model, the delays correspond with phase shifts in the initial functions for two dependent variables. The results of our researches show that when a instability-generating multienzymatic mechanism suffers variations of the delay time in any of its variables, a wide range of different dynamic responses can be produced. Our work is presented as an enlargement on the dynamic study of biochemical oscillations in general and, particularly, the glycolytic oscillations, under the consideration of the existence of variations in the phase shifts during the oscillations of metabolites involved in the studied reactive processes.