Protein kinase C (PKC) represents at present the paradigm for enzymes activated by lipids forming inverted non-lamellar phases, hexagonal phase H-II, in particular. Concerning the underlying molecular mechanism an important result was that it is the tendency to form and not the actual formation of the H-II phase (i.e. H-II propensity) which is critical. Lamellar membranes incorporating H-II phase forming lipids are under bending stress due to their negative spontaneous curvature. Such membranes are described as frustrated and are here defined to be in the L(epsilon) phase. This review summarizes current physical concepts regarding the L(epsilon) phase as well as the properties it imparts to membranes. A novel role for the L(epsilon) phase in peripheral lipid-protein interactions is described, resulting in the anchorage of proteins to lipid surfaces. In this mechanism one of the acyl chains of a phospholipid becomes intercalated into a hydrophobic site of the protein residing on the membrane surface, while the other chain remains in the bilayer. Accordingly, hydrophobic lipid-protein interaction is established yet without penetration of the protein into the bilayer. For eucaryotes modulation of H-II propensity in individual cellular organelle membranes is postulated to allow for the control of the membrane attachment and activity of specific sets of proteins contained in the said organelles. Finally, feasibility of the L(epsilon) phase as an ancient growth signal in procaryote and eucaryote cells is discussed, together with the possible role of this phase in maintaining the constitutive growth in cancer cells.