## ABSTRACT

In Section 4.1 we introduce the linearized oscillation results for a certain class of second order nonlinear delay differential equations. In Section 4.2 we present results on the existence of oscillatory solutions of the delay differential equation. In Section 4.3 we introduce Sturm comparison theorems which are very useful for the oscillation theory as well as the boundary value problems. In Section 4.4 we establish some oscillation criteria for second order neutral differential equations. By way of these criteria the oscillation problem for neutral differential equations can be reduced to the same problem for the corresponding delay equations and sometimes to the corresponding ordinary differential equation. In Section 4.5 we introduce the classification of nonoscillatory solutions for second order nonlinear neutral differential equations, various existence results of nonoscillatory solutions of different types are given. In Section 4.6, we present several bounded oscillation 203criteria for the second order neutral differential equation of unstable type. Section 4.7 deals with the forced oscillation. In Section 4.8 equations with nonlinear neutral terms are investigated. In the last section, advanced type equations are investigated, also a relation between the oscillation of equation of the advanced type and the oscillation of the corresponding ordinary differential equation is established.