For the pair of functional equations ( A ) ( r ( t ) y ′ ( t ) ) ′ + p ( t ) h ( h ( g ( t ) ) ) = f ( t ) and ( B ) ( r ( t ) y ′ ( t ) ) ′ − p ( t ) h ( y ( g ( t ) ) ) = 0 sufficient conditions have been found to cause all solutions of equation (A) to be oscillatory. These conditions depend upon a positive solution of equation (B).