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The co-adaptation of robots has been a long-standing research endeavour with the goal of adapting both body and behaviour of a system for a given task, inspired by the natural evolution of animals. Co-adaptation has the potential to eliminate costly manual hardware engineering as well as improve the performance of systems. The standard approach to co-adaptation is to use a reward function for optimizing behaviour and morphology. However, defining and constructing such reward functions is notoriously difficult and often a significant engineering effort. This paper introduces a new viewpoint on the co-adaptation problem, which we call co-imitation: finding a morphology and a policy that allow an imitator to closely match the behaviour of a demonstrator. To this end we propose a co-imitation methodology for adapting behaviour and morphology by matching state distributions of the demonstrator. Specifically, we focus on the challenging scenario with mismatched state- and action-spaces between both agents. We find that co-imitation increases behaviour similarity across a variety of tasks and settings, and demonstrate co-imitation by transferring human walking, jogging and kicking skills onto a simulated humanoid.