Gene category testing problems involve testing hundreds of null hypotheses that correspond to nodes in a directed acyclic graph. The logical relationships among the nodes in the graph imply that only some configurations of true and false null hypotheses are possible and that a test for a given node should depend on data from neighboring nodes. We developed a method based on a hidden Markov model that takes the whole graph into account and provides coherent decisions in this structured multiple hypothesis testing problem. The method is illustrated by testing Gene Ontology terms for evidence of differential expression.