In the univariate polynomial case there are only two notions of stability: Hurwitz stability for continuous polynomials, and Schur stability for discrete polynomials. However, in the multivariate polynomial case there exists a more complex situation since there are more classes of stability: Wide Sense Stable (WSS), Scattering Hurwitz Stable (SHS) and Strict Sense Stable (SSS) for continuous polynomials (Fettweis & Basu, 1987), and Wide Sense Schur Stable (WSSS), Scattering Schur (SS) and Strict Sense Schur Stable (SSSS) for discrete polynomials (Basu & Fettweis, 1987). These classes have different properties, for example some classes reduce to the Hurwitz or antiSchur univariate notion and some polynomials from some classes may lose their stability property in the presence of arbitrary small coefficient variations. Besides, between these classes has not been possible to establish a similar relationship as it does for Hurwitz and Schur univariate polynomials by the Moebius transformation (Bose, 1982). For a long time, SSS and SSSS polynomials have been employed to obtain key properties of stability and robust stability in their own domain because they have more coincident characteristics with Hurwitz and Schur univariate notions than the other multivariate classes have (Basu & Fettweis, 1987; Fettweis & Basu, 1987). Despite of this, in this work the interest is focused in two different notions of stability: Stable class for the continuous case (Kharitonov & Torres-Munoz, 1999), and Schur Stable class for the discrete case (TorresMunoz et al., 2006). The reason is twofold: firstly, both classes have the property of being the largest classes preserving stability when faced to arbitrary small coefficient variations, and secondly, it has been recently shown that any member of the Stable class is associated, by a bilinear transformation, to one member of the Schur Stable class in the same way that Hurwitz and Schur univariate polynomials are related by the Moebius transformation (Torres-Munoz et al., 2006). Besides, both classes are the natural extension of their univariate counterpart: Hurwitz and Schur univariate classes. In general, in the analysis and control of any system is important to have efficient, from the computational point of view, criteria to test the stability of its characteristic polynomial. For the univariate case, there is a big variety of well-known efficient algorithms to deal with the Hurwitz and Schur stabilities (Barnett, 1983; Parks & Hahn, 1992; Bhattacharyya, 1995). However, in the multivariate case this problem is more complex: in the m -variate ( 2 > m ) case there are few algorithms reported and they have the problem of their efficiency (Bose, 1982). Despite of this, in the bivariate ( 2 = m ) case there are a lot of algorithms to deal with the Schur Stable bivariate issue and some of them are efficient (Anderson & Jury, 1973;