Oscillations of neutral differential equations with variable coefficients

We obtain sufficient conditions for the oscillation of all solutions of the neutral differential equation d\dt [y(t) + P(t)y(t-T)] + Q(t)y(t-σ) = 0 where our results extend and improve several known results in the literature. These improvements and extensions are obtained by establishing and using some lemmas which are interesting in their own rights and which may have further applications in analysis.