Electronic Journal of Differential Equations, Vol. 2002(2002), No. 31, pp. 1-18. Title: Differential equations with several deviating arguments: Sturmian comparison method in oscillation theory, II Authors: Leonid Berezansky (Ben-Gurion Univ. of the Negev, Israel) Yury Domshlak (Ben-Gurion Univ. of the Negev, Israel) Abstract: We study the oscillation of solutions to the differential equation $$ \dot{x}(t) +a_1(t)x[r(t)]+a_2(t)x[p(t)]=0, \quad t\geq t_0 $$ which has a retarded argument $r(t)$ and an advanced argument $p(t)$. We obtain oscillation and non-oscillation conditions which are closed to be necessary. We provide examples to show that our results are best possible and compare them with known results. Submitted November 29, 2001. Published April 1, 2002. Math Subject Classifications: 34K11. Key Words: mixed differential equations, oscillation, non-oscillation, Sturmian comparison method. This and other articles are avilable in DVI, PDF, PS, and TeX format. Thanks to the European Mathematical Information Service, the EJDE and other journals have mirror copies through the world. Here is a partial listing of mirror sites. EUROPE: http://www.emis.de/journals/EJDE NORTH AMERICA: http://ejde.math.swt.edu http://ejde.math.unt.edu ftp: ejde.math.swt.edu (login: ftp) SOUTH AMERICA: http://www.icfes.gov.co/revistas/EJDE http://www.mat.unb.br/EMIS/journals/EJDE ASIA: http://www.kurims.kyoto-u.ac.jp/EMIS/journals/EJDE http://emis.math.ecnu.edu.cn/journals/EJDE AUSTRALIA: http://emis.maths.adelaide.edu.au/EMIS/journals/EJDE