The velocity distribution of stars in the solar neighbourhood can be globally characterized by the presence of two stellar streams (I and II). Stream I contains kinematic substructures, named moving groups of stars, such us the Pleiades and Hyades groups. While Stream II is essentially associated with the Sirius group. The origin and nature of these two stellar streams are still not completely clear. We propose that Streams I and II were gravitationally linked to an old gas supercloud that was disintegrated in parts that formed new subsystems, viz., the Orion arm and Gould's belt. On the basis of this idea, we constructed a dynamical model of the supercloud in order to explain the kinematic and structural characteristics of the local system of gas and stars. For the study of the relative orbits of the two stellar streams with respect to the supercloud's centre and of the Galactic orbit of the supercloud, we developed appropriate epicyclic motion equations. The results of the model indicate the possibility that about 75-100 Myr ago the supercloud crossed the Perseus arm and as a consequence was strongly braked. Besides, around 60 Myr ago, the position of the supercloud coincided approximately with that of the Big Dent, a huge depression of the Galactic disc. We suggest that the cause that originated the Big Dent could be the same that perturbed the supercloud starting the formation of the Orion arm and Gould's belt. In this context, we derived the theoretical distributions of positions and velocities for the stars of Streams I and II.