The paper discusses the asymptotic behaviour of all solutions of
the differential equation y˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t), t∈I=[t0,∞),
with a positive continuous function a, continuous functions
bi, f, and n continuously differentiable unbounded lags. We
establish conditions under which any solution y of this equation
can be estimated by means of a solution of an auxiliary functional
equation with one unbounded lag. Moreover, some related questions
concerning functional equations are discussed as well.