A new scheme for the modular control of discrete event systems is presented and studied. This scheme, called modular control with priorities (MCP), is an extension of earlier works on modular control in the realm of the supervisory control theory of discrete event systems. The key feature of this scheme is the use of a priority mechanism based on the priority functions of individual supervisors in the process of combining the control actions of individual supervisors. This approach is motivated by both theoretical and practical considerations. The main objective Is to use priority functions to mitigate or eliminate the problem of blocking that originates in conventional modular control. In this paper, we first show how to design individual supervisors so that they can operate under MCP. We then show how MCP operates and discuss the resulting properties of this approach. Finally, we present several algorithms for priority assignment to obtain nonblocking behavior under MCP. A motivating example from the area of telecommunications is used throughout the paper.