Distributed multimedia applications need convenient framework for their realiza tion in a distributed computer system. This paper deals with the problem of mapping distributed multimedia applications to a distributed computer system. An approach for formalization of this problem as well as a set of abstractions, mathematical pro gramming formulations, models and solution procedures are proposed. Distributed multimedia application is represented by one or a set of data flow graphs that specify quality of service and resource requirements of the application. Distri buted computer system is represented as a relevant directed weighted graph with information about available computer and communication resources. A problem of best placement (from the point of preliminary defined cost criteria) of data flow graphs onto distributed computer system is decided.