To understand the initial stages of membrane destabilization induced by viral proteins, the factors important for binding of fusion peptides to cell membranes must be identified. In this study, effects of lipid composition on the mode of peptides' binding to membranes are explored via molecular dynamics (MD) simulations of the peptide E5, a water-soluble analogue of influenza hemagglutinin fusion peptide, in two full-atom hydrated lipid bilayers composed of dimyristoyl- and dipalmitoylphosphatidylcholine (DMPC and DPPC, respectively). The results show that, although the peptide has a common folding motif in both systems, it possesses different modes of binding. The peptide inserts obliquely into the DMPC membrane mainly with its N-terminal alpha helix, while in DPPC, the helix lies on the lipid/water interface, almost parallel to the membrane surface. The peptide seriously affects structural and dynamical parameters of surrounding lipids. Thus, it induces local thinning of both bilayers and disordering of acyl chains of lipids in close proximity to the binding site. The "membrane response" significantly depends upon lipid composition: distortions of DMPC bilayer are more pronounced than those in DPPC. Implications of the observed effects to molecular events on initial stages of membrane destabilization induced by fusion peptides are discussed.