In this paper the problem of synthesizing deadlock-free modular supervisors for discrete-event systems is discussed, By introducing the d-invariant relation between a pair of supervisors, it is shown that when the control objective is described in terms of intersection of two languages, a necessary and sufficient condition for the modular supervisor to be deadlock-free is that this pair of subsupervisors satisfies a d-invariant relation, A procedure for synthesizing the deadlock-free modular supervisor is presented. Some issues concerning deadlock-free modular supervisory control are also discussed.