In this paper, by using Newton and Marclaurin inequalities we obtain some necessary conditions for a polynomial with positive coefficients to be Hurwitz stable, which generalize the recent results obtained in Borobia and Dormido (Linear Algebra Appl. 338 (2001) 67) and the proof of the result in this paper is much shorter than that of in Borobia and Dormido (Linear Algebra Appl. 338 (2001) 67). (C) 2003 Elsevier Ltd. All rights reserved.