Phospholipid bilayer membranes at prephase transition temperatures exhibit an increased permeability to solutes during exposure to static magnetic fields. A theoretical model of this magnetically induced membrane effect has been developed that is consistent with available experimental data. This model incorporates the fact that clusters (domains) of physically correlated lipid molecules form in bilayer membranes at prephase transition temperatures. The presence of these ripple structures produces an instability in the bilayer membrane elastic properties when the local radius of curvature approaches the critical value R /6, where R is the radius of the spherical liposome. As a result of this instability, the presence of weak external forces can produce major deformations of a liposome's shape and affect the permeation of water and solutes through the liposome's bilayer membrane. The theory is developed for the specific case of static magnetic field interactions with the diamagnetically anisotropic phospholipd molecules in bilayer membranes of spherical, unilamellar liposomes. Bilayer membrane transport of solutes and the magnetic birefringence of liposome suspensions are described in relation to the model of magnetic deformations. The applicability of the model to various types of external force fields is described. The magnetic deformation model is discussed in relation to other recent theories and experimental data on the sensitivity of artificial and natural bilayer membranes to electromagnetic fields in the prephase transition range.