Globally positive solutions for the third order differential equation with the damping term and delay, $$ x''' + q(t)x'(t) - r(t)f(x(\phi (t))) = 0, $$ are studied in the case where the corresponding second order differential equation $$ y'' + q(t)y = 0 $$ 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 in the case when (**) is nonoscillatory is given, as well.
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