The research on the origin of life, as such, seems to have reached an impasse as a clear and universal scientific definition of life is probably impossible. On the contrary, the research on the origin of evolution may provide a clue. But it is necessary to identify the minimum requirements that allowed evolution to emerge on early Earth. The classical approach, the 'RNA world hypothesis' is one way, but an alternative based on nonlinear dynamics dealing with far-from-equilibrium self-organization and dissipative structures can also be proposed. The conditions on early Earth, near deep-sea hydrothermal sites, were favorable to the emergence of dissipative structures such as vesicles with bilayer membranes composed of a mixture of amphiphilic and hydrophobic molecules. Experimentally these vesicles are able to self-reproduce but not to evolve. A plausible scenario for the emergence of a positive feedback process giving them the capability of evolving on early Earth is suggested. The possibilities offered by such a process are described in regard to specific characteristics of extant biological organisms and leads for future research in the field are suggested.