So, y ( t ) is continuous at the impulse points. Now, let y ( t ) be an eventually positive solution of inequality (6). Then y ( t ) > 0 , y ( t − τ ) > 0 , and y ([ t − 1]) > 0 for t > T. We will show that x ( t ) is an eventually positive solution of inequality (3). From (8), (9), and (6) we obtain that x ′ ( t ) + a ( t ) x ( t ) + b ( t ) x ( t − τ ) + c ( t ) x ([ t − 1]) Moreover, and So, x ( t ) is an eventually positive solution of inequality (3). The proof is complete. Following we give several sufficient conditions for the oscillation of equation (1)-(2). Theorem 2. If one of the following conditions is satisfied then every solution of equation (1)-(2) is oscillatory: 6 x ( t − i ) = ∏ T <t$_{j}$ ≤ t$_{i}$$_{−}$$_{1}$ (1 − b$_{j}$ ) − $^{1}$y ( t − i ) = ∏ T <t$_{j}$ ≤ t$_{i}$ (1 − b$_{j}$ ) − $^{1}$(1 − b$_{i}$ ) y ( t$_{i}$ ) = (1 − b$_{i}$ ) x ( t$_{i}$ ) x ( t + i ) = ∏ T <t$_{j}$ ≤ t$_{i}$ (1 − b$_{j}$ ) − $^{1}$y ( t + i ) = x ( t$_{i}$ ) . = ∏ T <t$_{j}$ ≤ t (1 − b$_{j}$ ) − $^{1}$y $^{′}$( t ) + a ( t ) ∏ T <t$_{j}$ ≤ t (1 − b$_{j}$ ) − $^{1}$y ( t ) + b ( t ) ∏ T <t$_{j}$ ≤ t − τ (1 − b$_{j}$ ) − $^{1}$y ( t − τ ) + c ( t ) ∏ T <t$_{j}$ ≤ [ t − 1] (1 − b$_{j}$ ) − $^{1}$y ([ t − 1]) = ∏ T <t$_{j}$ ≤ t (1 − b$_{j}$ ) − $^{1}$[ y $^{′}$( t ) + a ( t ) y ( t ) + B ( t ) y ( t − τ ) + C ( t ) y ([ t − 1])] ≤ 0 .