Double-end-anchored poly-ethylene-glycol-surfactants (DEA-PEG-surfactants) induce the gelation of lyotropic lamellar L-alpha phases stabilized by undulation forces. The physical hydrogel (L-alpha ,L-g) derives its viscoelasticity from the proliferation of defects at a mesoscopic level. The DEA-PEG-surfactants assume both looping and bridging conformations. The existence of novel bridging conformations is indicated by the coexistence of two lamellar phases and the limited swelling of the L-alpha and L-alpha ,L-g phases. Modeling of the polymer decorated membranes demonstrates the existence of bridging and yields a rapidly decreasing density of bridging conformations with increasing interlayer spacing.