Necessary conditions are derived for optimality of differential control processes in the presence of nondifferentiable state (or phase) constraints. The techniques of general Mathematical Programming and the Dubovitskii-Milyutin Theorem are employed. The necessary conditions derived are in the form of an adjoint integral equation and a pointwise maximal condition. It is found that the gradient of the state (or phase) constraint can be replaced by the Gateaux differential of a certain form in the adjoint equation.

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