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Coupled coincidence and fixed point problems have been in the focus of the research interest for last few years. The problem was introduced in fuzzy metric spaces only very recently. In this paper, we work out a weak coupled coincidence point theorem for a compatible pair of mappings in fuzzy metric spaces. As one of the corollaries we have a weak coupled fuzzy contraction mapping theorem. The space is endowed with a partial ordering. We use a combination of analytic and order theoretic concepts in the proof of our main theorem. The result is illustrated with an example.