We derive a weak Maximum Principle for nonsmooth optimal control problem involving mixed constraints under some convexity assumptions. Notably we consider problems with possibly nonsmooth mixed constraints. A nonsmooth version of the positive linear independence of the gradients with respect to the control of the mixed constraints plays a key role in validation of our main result.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)