We discuss the asymptotic performance of a multiterminal detection system comprising a central detector and two remote sensors that have access to discrete, spatially dependent, and temporally memoryless observations. We assume that prior to transmitting information to the central detector, each sensor compresses its observations at a rate which approaches zero as the sample size tends to infinity; and that on the basis of the compressed data from all sensors, the central detector seeks to determine whether the true distribution of the observations belongs to a null class II or an alternative class -----. Under the criterion that stipulates minimization of the type II error rate subject to an upper bound on the type I error rate, we obtain error exponents for four different problems in the above framework, and contrast our results with the case of simple hypothesis testing (| II | = |----| = 1).