Abstract. In this paper we consider the mixed integer general quadratic problem (MIGQP) that consists in maximizing a quadratic function subject to quadratic constraints, with three types of variables: binary, integer and real. Given a precision , we show how to associate two mixed integer linear programs and with MIGQP. The solution of gives an approximate solution of MIGQP while the solution of gives an upper bound for the optimal solution of MIGQP. The gap between these two solutions is an increasing function of . Some computational results, using a general-purpose mixed integer linear programming solver, are reported