In this talk, we discuss a system of ordinary differential equations with time-delay components, which are called delay-differential equations(DDEs). For a single equation of DDEs, we had already known the condition to obtain the asymptotic stability result, which is called stability condition. On the other hand, there are few results of the stability condition for a system of DDEs. Because the method used for a single equation of DDEs
(analysis of the characteristic equation) is difficult to apply to a system of DDEs. Under this situation, we introduce the different approach and derive new stability condition for the two component system of DDEs. Furthermore we apply this result to the initial value problem of a system of partial differential equations with time-delay terms. This method is a based on the weighted energy method. More precisely, we first rewrite a system of DDEs to the initial value and the dynamical boundary value problem of the partial differential equations. Then we apply the energy method to this problem and derive the stability condition.