We give necessary and sufficient conditions such that the homogeneous differential equations of the type: $$(r(t)x^{prime}(t))^{prime}+q(t)x^{prime}(t)+p(t)x(t)=0$$ are nonoscillatory where $r(t)$ > 0 for $t{in}I=[{alpha},{infty})$, ${alpha}$ > 0. Under the suitable conditions we show that the above equation is nonoscillatory if and only if for ${gamma}$ > 0, $$(r(t)x^{prime}(t))^{prime}+q(t)x^{prime}(t)+p(t)x(t-{gamma})=0$$ is nonoscillatory. We obtain several comparison theorems.