Summary: We introduce multivariate generalizations of the Bernstein-Szegö polynomials, which are associated to the root systems of the complex simple Lie algebras. The multivariate polynomials in question generalize Macdonald’s Hall-Littlewood polynomials associated with root systems. For the root system of type \(A_{1}\) (corresponding to the Lie algebra \(\mathfrak {sl} (2; \mathbb C))\) the classic Bernstein-Szegö polynomials are recovered.