Abstract. The authors consider the equation (E) $(x(t)+\lambda x(t-\tau ))^{(n)} + f(t,x(g(t))) = 0,$ where $ \lambda\not= 0$, $\tau >0$, $f$ and $g$ are continuous, $g(t) \le t$, and $\lim_{t\to +\infty }g(t) = + \infty $. They give sufficient conditions for (E) to have an oscillatory solution, and in addition, give an asymptotic expression for this oscillatory solution involving the sine function and an exponential.

AMS Subject Classification (1991): 34K15, 34K40

Received May 8, 1998, and in revised form April 2, 1999. (Registered under 2721/2009.)