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An approach to image composition and animation with procedural models which uses data-flow concepts is presented. The characteristics of procedural models and data-flow theory are reviewed. The concept of procedural coherency is introduced, and a general method for `in-betweening' with procedural models is presented. When such models are described as functions, their composition into pictures can be represented hierarchically. The network representing such a composition is a data-flow graph whose nodes are procedural models. This interpretation, best described as a data-flow approach to the representation of compositions, facilitates parallelism. For applications that use the same network repeatedly, this method can greatly shorten computation times. In environments where diverse computers must interact to produce a final result, this method can be used to organize and coordinate the necessary interactions in a natural, high-level way. A software system, SCORE, is described which supports composing and animating in a simulated data-flow environment. The approach allows compositions to manipulate any computer-controlled media, such as music synthesizers and editors.