Let $\gamma$ be an integral solution of an analytic real vector field $\xi$ defined in a neighbordhood of $0\in {ℝ}^3$. Suppose that $\gamma$ has a single limit point, $\omega \left(\gamma \right)=\left\{0\right\}$. We say that $\gamma$ is non oscillating if, for any analytic surface $H$, either $\gamma$ is contained in $H$ or $\gamma$ cuts $H$ only finitely many times. In this paper we give a sufficient condition for $\gamma$ to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property for...