Globally positive solutions for the third order differential equation with the damping term and delay, $$x^{\text{'}\text{'}\text{'}}+q\left(t\right)x^{\text{'}}\left(t\right)-r\left(t\right)f\left(x\left(\phi \left(t\right)\right)\right)=0,$$ are studied in the case where the corresponding second order differential equation $$y^{\text{'}\text{'}}+q\left(t\right)y=0$$ is oscillatory. Necessary and sufficient conditions for all nonoscillatory solutions of (*) to be unbounded are given. Furthermore, oscillation criteria ensuring that any solution is either oscillatory or unbounded together with its first and second derivatives are presented. The comparison of results with those...