We propose an algorithm for the classification of fluorescence microscopy images depicting the spatial distribution of proteins within the cell. The problem is at the forefront of the current trend in biology towards understanding the role and function of all proteins. The importance of protein subcellular location was pointed out by Murphy, whose group produced the first automated system for classification of images depicting these locations, based on diverse feature sets and combinations of classifiers. With the addition of the simplest multiresolution features, the same group obtained the highest reported accuracy of 91.5% for the denoised 2D HeLa data set. Here, we aim to improve upon that system by adding the true power of multiresolution - adaptivity. In the process, we build a system able to work with any feature sets and any classifiers, which we denote as a Generic Classification System (GCS). Our system consists of multiresolution (MR) decomposition in the front, followedby feature computation and classification in each subband, yielding local decisions. This is followed by the crucial step of combining all those local decisions into a global one, while at the same time ensuring that the resulting system does no worse than a no-decomposition one. On a nondenoised data set and a much smaller number of features (a combination of texture and Zernicke moment features) and a neural network classifier, we obtain a high accuracy of 89.8%, effectively proving that the space-frequency localized information in the subbands adds to the discriminative power of the system.