We have studied the photopolymerization of an amphiphilic compound containing a biphenyl group which has, at one end, a fumarate propyl ester and, at the other, a vinyl group. We have photopolymerized the compound when it was spread as a monolayer at the air/water interface and have then assembled it into multilayer structures by the Langmuir-Blodgett technique. We have also formed multilayers of the monomers and then photopolymerized them. Both kinds of films have been characterized by X-ray diffraction, by polarizing microscopy, and by UV absorption spectroscopy. When monomers are assembled into a layer structure and are then irradiated with UV light, they will only polymerize when in the smectic phase, which-can be produced by heating the film to a temperature above 54 degrees C, but when the multilayer consists of two-dimensional crystals, it will not polymerize. Because polymerization can take place at the air/water interface, we think it likely that the polymerization process takes place within layers rather than between layers.