We establish some new criteria for the oscillation of third-order difference equations of the form Δ ( ( 1 / a 2 ( n ) ) ( Δ ( 1 / a 1 ( n ) ) ( Δ x ( n ) ) α 1 ) α 2 ) + δ q ( n ) f ( x [ g ( n ) ] ) = 0 , where Δ is the forward difference operator defined by Δ x ( n ) = x ( n + 1 ) − x ( n ) .