We propose evolutionary scenarios in which double degenerate white dwarf systems can be produced through one or two phases of stable mass transfer. We consider Algol-type evolution as well as evolution involving first a stage of common-envelope (CE) evolution followed by a phase of stable mass transfer. We also show that the final orbital period of double white dwarf systems depends on the period after the first phase of mass transfer, and that there is critical period (the bifurcation period) above which systems evolve to orbital periods of the order of days and below which systems evolve towards very short orbital periods (a few hours). This probably corresponds to the observation that double degenerate systems have periods either of hours or of days. We also find a limit on the stability of mass transfer for systems that first go through a phase of CE evolution. We suggest that our new evolutionary scheme involving two stages of stable mass transfer and our scheme involving first CE evolution followed by stable mass transfer should be included in population synthesis models.