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In the present paper the exhaustive topological classification of nonsingularMorse-Smale flows of $n$-manifolds with two limit cycles is presented.Hyperbolicity of periodic orbits implies that among them one is attracting andanother is repelling. Due to Poincare-Hopf theorem Euler characteristic ofclosed manifold $M^n$ which admits the considered flows is equal to zero. Onlytorus and Klein bottle can be ambient manifolds for such flows in case of$n=2$. Authors established that there exist exactly two classes of topologicalequivalence of such flows of torus and three of the Klein bottle. There are noconstraints for odd-dimensional manifolds which follow from the fact that Eulercharacteristic is zero. However, it is known that orientable $3$-manifoldadmits a flow of considered class if and only if it is a lens space. In thispaper, it is proved that up to topological equivalence each of $\mathbb S^3$and $\mathbb RP^3$ admit one such flow and other lens spaces two flows each.Also, it is shown that the only non-orientable $n$-manifold (for $n>2$), whichadmits considered flows is the twisted I-bundle over $(n-1)$-sphere. Moreover,there are exactly two classes of topological equivalence of such flows. Amongorientable $n$-manifolds only the product of $(n-1)$-sphere and the circle canbe ambient manifold of a considered flow and the flows are split into twoclasses of topological equivalence.

Nonsingular Morse-Smale flows of n-manifolds with attractor-repeller dynamics