We propose evolutionary scenarios in which double degenerate white dwa
rf systems can be produced through one or two phases of stable mass tr
ansfer. We consider Algol-type evolution as well as evolution involvin
g 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 phas
e of mass transfer, and that there is a critical period (the bifurcati
on period) above which systems evolve to orbital periods of the order
of days and below which systems evolve towards very short orbital peri
ods (a few hours). This probably corresponds to the observation that d
ouble degenerate systems have periods either of hours or of days. We a
lso find a limit on the stability of mass transfer for systems that fi
rst go through a phase of CE evolution. We suggest that our new evolut
ionary scheme involving two stages of stable mass transfer and our sch
eme involving first CE evolution followed by stable mass transfer shou
ld be included in population synthesis models.