Motivated by the increasing interest in models which consider scalar fields as viable dark matter candidates, we have constructed a generalization of relativistic Boson Stars (BS) composed of two coexisting states of the scalar field, the ground state and the first excited state. We have studied the dynamical evolution of these Multi-state Boson Stars (MSBS) under radial perturbations, using numerical techniques. We show that stable MSBS can be constructed, when the number of particles in the first excited state, N2, is smaller than the number of particles in the ground state, N1. On the other hand, when N2 > N1, the configurations are initially unstable. However, they evolve and settle down into stable configurations. In the stabilization process, the initially ground state is excited and ends in a first excited state, whereas the initially first excited state ends in a ground state. During this process, both states emit scalar field radiation, decreasing their number of particles. This behavior shows that even though BS in the first excited state are intrinsically unstable under finite perturbations, the configuration resulting from the combination of this state with the ground state produces stable objects. Finally we show in a qualitative way, that stable MSBS could be realistic models of dark matter galactic halos, as they produce rotation curves that are flatter at large radii than the rotation curves produced by BS with only one state.

14 pages. Extended discussion and new figures added. Conclusions unchanged. Accepted for publication in Physical Review D