Here we derive necessary conditions of optimality for optimal control problems with both state and mixed constraints in the form of nonsmooth maximum principle. A special feature of our main result is that the mixed constraints may appear in both the equality and inequality form. These conditions are stated in terms of a "joint" subdifferential with respect to both state and control variables. The use of the "joint" subdifferential gives sufficiency for normal, linear convex problems as it can be interfered by an adaptation of [7].