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Problem frames are a systematic approach to the decomposition of problems that allows us to relate requirements, domain properties, and machine specifications. Having decomposed a problem, one approach to solving it is through a process of composing solutions to sub-problems. In This work, we contribute to supporting such a process by providing a way to compose multiple problem frames. We develop a systematic approach to composing inconsistent requirements. We introduce composition frames, a requirements construct that models relevant aspects of composition and thus deals with unwanted effects, such as interference of overlapping reactions to events. Throughout the paper, we use a simple case study to illustrate and validate our ideas.