Abstract The potential kinetic complexity of polymeric regulatory enzymes does not seem to be often expressed in nature. Most of these enzymes exhibit in fact a rather simple kinetic behaviour. This functional simplicity is probably the consequence of constraints between rate constants or of blocking of some reaction steps. Functional simplicity is believed to have emerged in the course of neo-Darwinian evolution as a consequence of a trend towards an improved functional efficiency. Functional efficiency may be reached, in polymeric regulatory enzymes, when either of the two sets of conditions are met. The first set of conditions implies the occurrence of the unicity of enzyme conformation in any transition state, a loose coupling between subunits and an exact balance of the driving forces exerted by the enzyme in the forward and backward directions of the catalytic step. This situation results in constraints between rate constants which allow degenerescence of the steady state rate equation. The second set of conditions involves again the unicity of enzyme conformation in any of the transition states, associated with a tight coupling of subunits, and a driving force exerted by the enzyme much strongly in the forward than in the backward direction of the catalytic step. These conditions imply blocking of some reaction steps and again degenerescence of the corresponding rate equation. The most frequent types of quaternary structure and subunit interactions, namely loose coupling between subunits, and tight coupling associated with conservation of at least one symmetry axis, have probably emerged as molecular organizations, which precisely allow both functional efficiency and simplicity to occur. Indeed these situations probably represent the term of two different evolutionary trends. Therefore enzymes that have not reached this state usually exhibit more complex kinetic behaviour. Wavy curves, “bumps” and turning points may be considered as manifestations of the ancestral character of an enzyme.