Oscillatory and Asymptotic Behavior of Damped Functional Differential Equations

New theorems on the oscillatory and asymptotic behavior of solutions of the damped differential equations with deviating arguments of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} x^{.} ({\rm t) +}p(t)x^. [\sigma (t)] + q(t)f(x[g(t)]) = 0\;\left({^. = \frac{d}{{dt}}} \right), \\ x^{.} ({\rm t) +}p(t)x^. [\sigma (t)] + q(t)f(x[g(t)]) = 0 \\ \end{array} $$\end{document}are established.