A remark on the ODE with two discrete delays

The aim of this paper is to outline a formal framework for the analytical analysis of the Hopf bifurcations in the delay differential equations with two independent time delays. Some results for the differential– difference equations with two delays, when the both of the coefficients of linearized equation are negative were obtained in [X. Li, S. Ruan, J. Wei, Stability and bifurcation in delay-differential equations with two delays, J.Math. Anal. Appl. 236 (1999) 254–280]. In the paper we present some remarks on the case studied in [X. Li, S. Ruan, J.Wei, Stability and bifurcation in delay-differential equations with two delays, J. Math. Anal. Appl. 236 (1999) 254–280] and also two other cases, namely when the coefficients of linearized equation have different signs and when coefficients are both positive. © 2006 Elsevier Inc. All rights reserved