This paper presents the solution to the output feedback mixed H2/H∞ control problem via the solution of an associated Nash game. Considering a two-player nonzero sum game, two performance criteria are used, one reflecting an H∞ constraint and the another reflecting an H2 optimality requirement. Assuming that the mixed H2/H∞ controller has the separation structure of H2 and H∞ controllers, the feedback and observer gains of the mixed H2/H∞ controller are determined by solving five coupled Ricatti equations.