  In this letter we introduce a class of delayed kinetic systems derived from
mass action type reaction network models. We define the time delayed positive
stoichiometric compatibility classes and the notion of complex balanced time
delayed kinetic systems. We prove the uniqueness of equilibrium solutions
within the time delayed positive stoichiometric compatibility classes for such
models. In our main result we prove the semistability of the equilibrium
solutions for complex balanced systems with arbitrary time delays using an
appropriate Lyapunov-Krasovskii functional and LaSalle's invariance principle.
As a consequence, we obtain that every positive complex balanced equilibrium
solution is locally asymptotically stable relative to its positive
stoichiometric compatibility class.
