The fusion of lipid membranes involves major changes of the membrane curvatures and is mediated by fusion proteins that bind to the lipid membranes. For a better understanding of the way fusion proteins steer this process, we have studied the interaction of two different viral fusion peptides, HA2-FP and TBEV-FP, with monoolein mesophases as a function of temperature and pressure at limited hydration. The fusion peptides are derived from the influenza virus hemagglutinin fusion protein (HA2-FP) and from the tick-borne encephalitis virus envelope glycoprotein E (TBEV-FP). By using synchrotron X-ray diffraction, the changes of the monoolein phase behavior upon binding the peptides have been determined and the concomitant secondary structures of the peptides have been analyzed by FTIR spectroscopy. As main results we have found that the fusion peptides interact differently with monoolein and change the pressure and temperature dependent lipid phase behavior to different extents. However, they both destabilize the fluid lamellar phase and favor phases with negative curvature, i.e. inverse bicontinuous cubic and inverse hexagonal phases. These peptide-induced phase changes can partially be reversed by the application of high pressure, demonstrating that the promotion of negative curvature is achieved by a less dense packing of the monoolein membranes by the fusion peptides. Pressure jumps across the cubic-lamellar phase transition reveal that HA2-FP has a negligible effect on the rates of the cubic and the lamellar phase formation. Interestingly, the secondary structures of the fusion peptides appear unaffected by monoolein fluid fluid phase transitions, suggesting that the fusion peptides are the structure dominant species in the fusion process of lipid membranes.