  We investigate the topological structure of flows on the Girl's surfaces
which is one of two possible immersions of the projective plane in
three-dimensional space with one triple point of the selfintersection. First,
we describe the cellular structure of the Boy's and Girl's surfaces and prove
that there are unique images of the project plane in the form of a 2-disc, in
which the opposite points of the boundary are identified and this boundary
belongs to the preimage of the 1-skeleton of the surface. Second, we described
three structures of flows with one fixed point and no separatrix on the Girl's
surface and proved that there are no other such flows. Third, we proved that
Morse-Smale flows and they alone are structurally stable on the Boy's and
Girl's surfaces. Fourth, we have found all possible structures of optimal
Morse-Smale flows on the Girl's surface. Fifth, we have obtained a
classification of Morse-Smale flows on the projective plane, that immersed on
the Girl's surface. And finally, we described the components of linear
connectivity of sets of these flows
