We investigate the location of poles of neutral systems with many chains of poles asymptotic to same points on the imaginary axis, this question being the first step towards stability analysis. In many cases, chains of poles are located on both sides of the imaginary axis implying then instability. © 2012 IFAC.10PART 1120125 IFAC TC 2.2. Linear Control Systems,IFAC TC 2.3. Non-Linear Control Systems,IFAC TC 2.5. Robust Control,IFAC TC 2.1. Control Design,IFAC TC 1.5. Networked SystemsBellman, R., Cooke, K.L., (1963) Differential-Difference Equations, , Academic Press, New York, LondonBonnet, C., Fioravanti, A.R., Partington, J.R., Stability of neutral systems with commensurate delays and poles asymptotic to the imaginary axis (2011) SIAM Journal on Control and Optimization, 49, pp. 498-516Michiels, W., Niculescu, S.I., (2007) Stability and Stabilization of Time-Delay Systems, , Society for Industrial & Applied Mathematics,U.SPontryagin, L.S., On the zeros of some elementary transcendental functions (1955) American Mathematical Society Transactions, 2, pp. 95-110Richard, J.P., Time-delay systems: An overview of some recent advances and open problems (2003) Automatica, 39, pp. 1667-1694Vyhlídal, T., Zítek, P., Quasipolynomial mapping based rootfinder for analysis of time delay systems (2003) Proceedings of the IFAC Workshop on Time-Delay Systems (TDS'03, Rocquencourt), , Rocquencourt, France