  We develop an abstract framework for obtaining optimal rates of mixing and
higher order asymptotics for infinite measure semiflows. Previously, such
results were restricted to the situation where there is a first return
Poincar\'e map that is uniformly expanding and Markov. As illustrations of the
method, we consider semiflows over nonMarkov Pomeau-Manneville intermittent
maps with infinite measure, and we also obtain mixing rates for semiflows over
Collet-Eckmann maps with nonintegrable roof function.
