Some new criteria for the oscillation of first-order forced nonlinear difference equations of the form Δ x ( n ) + q 1 ( n ) x μ ( n + 1 ) = q 2 ( n ) x λ ( n + 1 ) + e ( n ) , where λ , μ are the ratios of positive odd integers 0 < μ < 1 and λ > 1 , are established.