The n -th order nonlinear functional differential equation [ r ( t ) x ( n − υ ) ( t ) ] ( υ ) = f ( t , x ( g ( t ) ) ) is considered; necessary and sufficient conditions are given for this equation to have: (i) a positive bounded solution 0 \]"> x ( t ) → B > 0 as t → ∞ ; and (ii) all positive bounded solutions converging to 0 as t → ∞ . Other results on the asymptotic behavior of solutions are also given. The conditions imposed are such that the equation with a discontinuity 0$" display="block"> [ r ( t ) x ( n − υ ) ( t ) ] ( υ ) = q ( t ) x − λ ,       λ > 0 is included as a special case.