We prove versions of the Feller-Miyadera-Phillips theorem characterizing the generators of positive _C_0- and _C_0*-semigroups on ordered Banach spaces, for which the norm and dual norm are monotonic. Two proofs are given. The first is based on half-norm theory whilst the second exploits the existence of an equivalent Riesz norm. This latter norm exists if, and only if, the positive cone is normal and generating.