The paper discusses the asymptotic behaviour of all solutions of
the differential equation $\dot y(t)=-a(t)y(t) +\sum_{i=1}^{n}b_i(t)y(\tau_i(t))+f(t)$ , $t\in I=[t_0,\infty)$ ,
with a positive continuous function $a$ , continuous functions
$b_i$ , $f$ , 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.