For the equation L_nv(t) + a(t)h(y(g(t))) = f(t) where L_ny(t)=p_n(t)(p_(n-1_(t)(...(p_1(t)(p_0(t)y(t))')'...)')'sufficient conditions have been found for all of its solutions to be oscillatory. The conditions found also lead to growth estimates for the nonoscillatory solutions.