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We prove a strong converse for a class of source coding problems. In each member of this class, there is one node that has access to all of the source sequences. This node has a direct link to every other node that can observe one or more source sequences. Source sequences are drawn i.i.d. according to a given distribution on a finite alphabet. The distortion measure is finite. The strong converse discussed here states that if a given rate vector R is not D-achievable, then for any sequence of block codes at rate R the probability of observing distortion no greater than D decreases exponentially to 0 as the code dimension grows without bound. The result can be applied to prove the strong converse for the Gray-Wyner problem and the multiple description problem.