This paper is concerned with an impulsive neutral differential equation of Euler form with unbounded delays ddt[x(t)-C(t)x(αt)]+P(t)tx(βt)=0, t<t0>0,t≠tk,x(tk)=bkx(tk-) +(1-bk)∫βtktkP(sβ)sx(s)ds,k=1,2,. ... Sufficient conditions are obtained for every solution of (*) to tend to a constant as t→∞. ©2011 Elsevier Ltd. All rights reserved.