Coevolutionary networks can encapsulate information about the dynamics of presence and absence of gene families in organisms. Analysis of such networks should reveal fundamental principles underlying the evolution of cellular systems and the functionality of sets of genes. In this study, we describe a new approach for analyzing coevolutionary networks. Our method detects Mutually Exclusive Orthologous Modules (MEOMs). A MEOM is composed of two sets of gene families, each including gene families that tend to appear in the same organisms, such that the two sets tend to mutually exclude each other (if one set appears in a certain organism the second set does not). Thus, a MEOM reflects the evolutionary replacement of one set of genes by another due to reasons such as lineage/environmental specificity, incompatibility, or functional redundancy. We use our method to analyze a coevolutionary network that is based on 383 microorganisms from the three domains of life. As we demonstrate, our method is useful for detecting meaningful evolutionary clades of organisms as well as sets of proteins that interact with each other. Among our results, we report that: 1) MEOMs tend to include gene families whose cellular functions involve transport, energy production, metabolism, and translation, suggesting that changes in the metabolic environments that require adaptation to new sources of energy are central triggers of complex/pathway replacement in evolution. 2) Many MEOMs are related to outer membrane proteins, such proteins are involved in interaction with the environment and could thus be replaced as a result of adaptation. 3) MEOMs tend to separate organisms with large phylogenetic distance but they also separate organisms that live in different ecological niches. 4) Strikingly, although many MEOMs can be identified, there are much fewer cases where the two cliques in the MEOM completely mutually exclude each other, demonstrating the flexibility of protein evolution. 5) CO dehydrogenase and thymidylate synthase and the glycine cleavage genes mutually exclude each other in archaea; this may represent an alternative route for generation of methyl donors for thymidine synthesis.