Clustering is a fundamental data analysis step that consists of producing a partition of the observations to account for the groups existing in the observed data. In this paper, we introduce an additional cooperative aspect. We address cases in which the goal is to produce not a single partition but two or more possibly related partitions using cooperation between them. Cooperation is expressed by assuming the existence of two sets of labels (group assignments) which are not independent. We also model additional interactions by considering dependencies between labels within each label set. We propose then a cooperative setting formulated in terms of conditional Markov Random Field models for which we provide alternating and cooperative estimation procedures based on variants of the Expectation Maximization (EM) algorithm for inference. We illustrate the advantages of our approach by showing its ability to deal successfully with the complex task of segmenting simultaneously and cooperatively tissues and structures from MRI brain scans.