We investigated the phase behavior of double-tail lipids, as a function of temperature, headgroup interaction and tail length. At low values of the head-head repulsion parameter a(hh), the bilayer undergoes with increasing temperature the transitions from the subgel phase L-c via the flat gel phase L-beta to the fluid phase L-alpha For higher values of a(hh), the transition from the L-c to the L-alpha phase occurs via the tilted gel phase L-beta ' and the rippled phase P-beta '. The occurrence of the L-beta ' phase depends on tail length. We find that the rippled structure (P-beta ') occurs if the headgroups are Sufficiently surrounded by water and that the ripple is a coexistence between the L-c or L-beta ' phase and the L-alpha phase. The anomalous swelling, observed at the P-beta ' -> L-alpha transition, is not directly related to the rippled phase, but a consequence of conformational changes of the tails.