For deterministic hybrid flow lines with multiple classes of customer and no overtaking, we develop upper bounds on the customer departure times. For this general class of systems, the bounds are the most that one can deduce; examples can be constructed where equality is achieved and where it is not. We incorporate a very general class of setups and similarly obtain upper bounds. Such hybrid flow lines are natural candidates to serve as models of cluster tools in semiconductor wafer manufacturing. We use the flow lines as a starting point for the development of approximation models for a relatively new class of cluster tools with linear flow, called linear cluster tools. The approximations include issues caused by wafer transport robots and rolling setups. The resulting approximations are of good quality; they predict the just-in-time (maximum) throughput to within about 5%. Computation requires two orders of magnitude less effort than detailed simulation. They may thus be useful for fabricator simulations.