Alexander's Subbase Theorem is generalized for partially ordered sets. Our generalization is nontrivial inasmuch as Alexander's Theorem pertains to the partially ordered set (T, ∪) whereT is the set of all the open sets of a topological space and thus $$(\overline T ,\underline C )$$ is a complete partially ordered set which is also join infinite distributive, whereas here our generalization pertains to any partially ordered set with a maximum 1 and which satisfies the rather weak «distributivity» condition given by (1) below.