A theory of the coupling of photons to the exciton states of a monomolecular layer is presented. It is shown that the collective excitations (polaritons) of the layer are of mixed exciton-photon character. For transitions polarized perpendicular to the exciton wave vector there are two polariton branches, one is superradiant with radiative lifetimes ${\left(\frac{\lambda }{a}\right)}^2\simeq {10}^4$ times shorter than for the free molecule, and the other does not radiate at all. This subradiant branch is defined for all frequencies $\omega$ below the molecular transition frequency ${\omega }_0$ and for $\omega \ll {\omega }_0$ corresponds to an electromagnetic wave trapped on the monolayer. The properties of polaritons on monolayers near the plane interface of two media are considered and the polariton dispersion relation examined for some special cases.

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