Functionally related genes co-evolve, probably due to the strong selection pressure in evolution. Thus we expect that they are present in multiple genomes. Physical proximity among genes, known as gene team, is a very useful concept to discover functionally related genes in multiple genomes. However, there are also many gene sets that do not preserve physical proximity. In this paper, we generalized the gene team model, that looks for gene clusters in a physically clustered form, to multiple genome cases with relaxed constraint. We propose a novel hybrid pattern model that combines the set and the sequential pattern models. Our model searches for gene clusters with and/or without physical proximity constraint. This model is implemented and tested with 97 genomes (120 replicons). The result was analyzed to show the usefulness of our model. Especially, analysis of gene clusters that belong to B. subtilis and E. coli demonstrated that our model predicted many experimentally verified ope...