We begin by proving that a locally free \,$C^{2}$-action of \,$\mathbb{R}^{n-1}$\, on \,$T^{n-1}\times [0,1]$\, tangent to the boundary and without compact orbits in the interior has all non-compact orbits of the same topological type. Then, we consider the set \,$A^{2}(\mathbb{R}^{n},N)$\, of \,$C^{2}$-actions of \,$\mathbb{R}^{n}$\, on a closed connected orientable real analytic \,$n$-manifold \,$N.$\, We define a subset \,$\mathscr{A}_{n}\subset A^{r}(\mathbb{R}^{n},N)$\, and prove that if \,$\varphi \in \mathscr{A}_{n}$\, has a \,$T^{n-1}\times \mathbb{R}$-orbit, then every \,$n$-dimensional orbit is also a \,$T^{n-1}\times \mathbb{R}$-orbit. The subset \,$\mathscr{A}_{n}\,,$\, is big enough to contain all real analytic actions that have at least one \,$n$-dimensional orbit. We also obtain information on the topology of \,$N.$\.