Optimality conditions for control problems with mixed state-control constraints have been the focus of attention for a long time. In particular, the subject of necessary conditions in the form of maximum principles have been addressed by a number of authors; see for example [1–4], to name but a few. Weak maximum principles, which apply to weak local solutions, covering problems with possibly nonsmooth data, have been considered in [5] and, in a more general setting, in [3]. For nonsmooth problems, strong maximum principles, which in turn apply to “strong” local solutions, have also received some attention recently (see [6,7]). Various recent results, including those of the present paper, can be captured as special cases of the following optimal control problem with mixed constraints, also known as