For the equation L n v ( t ) + a ( t ) h ( y ( g ( t ) ) ) = f ( t ) where L n y ( t ) = p n ( t ) ( p n − 1 ( t ) ( … ( p 1 ( t ) ( p o ( 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 tle nonoscillatory solutions.