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The Berezinskii-Kosterlitz-Thouless (BKT) theorem predicts that two-dimensional bosonic condensates exhibit quasi-long-range order which is characterized by a slow decay of the spatial coherence. However previous measurements on exciton-polariton condensates revealed that their spatial coherence can decay faster than allowed under the BKT theory, and different theoretical explanations have already been proposed. Through theoretical and experimental study of exciton-polariton condensates, we show that the fast decay of the coherence can be explained through the simultaneous presence of multiple modes in the condensate.