Many organic materials (disordered and crystalline as well) have rather broad and dispersionless electronic resonances. The excitations in these materials are localized, and thus for these excitations the wave vector is not a “good” quantum number. We analyze the optical properties of exciton polaritons in a microcavity, which utilize such organic materials as the optically active semiconductor. We show that as a result of strong light-matter coupling two polariton branches appear in the microcavity, which are analogous to the cavity-polariton branches observed in inorganic semiconductor structures. However, in contrast to the case of polaritons in inorganic semiconductors, the lower polariton branch exists only in a certain restricted intervals of wave vector values. We also show that in such materials the majority of the electronic excited states do not strongly couple to the cavity photon, and these states can be regarded as essentially incoherent. Applying this physical picture for the microcavities containing disordered cyanine dye J aggregates, we examine the decay of the upper cavity polaritons accompanied by the emission of an intramolecular phonon. We show that the main contribution to the upper polariton nonradiative decay rate arises from the transition to incoherent states, and the transition is very fast (of the order of 50 fs). From the results of our calculations we discuss the dynamics of excitations in a microcavity containing organic materials