We give a linear characterization of the convex hull of the disjunction of polymatroids. For the family of inequalities defining the convex hull, we present an efficient separation algorithm. Among consequences of this result are the characterization of the convex hull of matroid polyhedra [Conforti/Laurent 88], and the characterization of the convex hull of 0-1 points satisfying logical conditions called cardinality rules [Yan/Hooker 99, Balas 2000].