In this paper we provide an algebraic method for the design of an appropriate transfer function making simultaneously two polynomials strictly positive real(SPR), in the so-called robust SPR problem for two polynomials. This problem arises in the design of recursive estimation algorithms used for identification purposes and in active noise control(ANC) applications. In the former a given transfer function involving the poles of the unknown transfer function must be made SPR, in the Latter, the phase of a transfer function must be matched within a range of (- pi /2, pi /2). Robust SPR design methods try to fulfill the phase requirements for all possible transfer functions belonging to a given uncertainty description. Here we focus on uncertainties described by two polynomials.