We have built an experimental set-up allowing us to measure photoconduction in the plane of single monolayers. The monolayers are deposited by the Langmuir-Blodgett technique onto a quartz plate with two interdigitated electrodes. The electrode separation distance is 10 mu m, smaller than the typical domain size in the studied monolayers. This enables one to perform photoconduction measurements through single two-dimensional crystals. Water-soluble charged cyanine dyes can be adsorbed onto an oppositely charged monolayer. These molecules form monocrystalline rectangular domains of typical size 100 X 20 mu m(2). The photoconduction of these domains is studied here. The photoconduction spectrum follows the absorption spectrum of the system (but with a better efficiency for the aggregate bands) indicating that the charge carrier generation occurs through exciton dissociation. When using a polymerizable monolayer, the photoconduction process is greatly altered after polymerisation : the relaxation time of the photocurrent is two orders of magnitude faster and the spectrum shows an additional band at shorter wavelength where almost no absorption takes place.