A theory of the exciton spontaneous emission from a semiconductor slab with strong exciton-photon interaction is developed. The limit of the radiative decay rate G large compared to the exciton-phonon scattering rate g is studied for the first time. It is shown that simultaneous account for the structural disorder and exciton-acoustic phonon scattering results in a two-exponential photoluminescence decay under off-resonant pulse excitation. In a well-organized structure (weak disorder), the fast component determined by G can lead to ultrafast photoluminescence decay with the lifetime of tens of fs. In a strongly disordered structure the decay turns out to be one-exponential and independent of G, in accordance with recent experimental results.The possibility of ultrafast radiative recombination of excitons in semiconductor structures has attracted much attention in recent years due to its crucial role for high-performance optoelectronic applications. One way to increase the exciton radiative decay rate G is to utilize an optically active material with strong exciton-photon interaction, such as semiconductor-insulator superlattices [1]. Although the exciton radiative recombination has been intensively studied in literature (see, e.g., Ref.[2] and references therein), only the situation of G ( g (g is the exciton-phonon scattering rate), which is typical for III-V semiconductors, has been considered.In the present work we examine the opposite case of G ) g typical for materials with strong exciton-photon coupling. Although the main results of our study are quite general for such kind of systems, concrete calculations are made for a homogeneous slab of (phenethylammonium) 2 PbI 4 (PEPI) in vacuum, with the following model parameters [3]: longitudinal-transverse splitting hD LT ¼ 40 meV, exciton transverse energy hw ex ¼ 2:4 eV, high-frequency background dielectric constant e b ¼ 4, and the exciton dephasing time g À1 ¼ 0:2 ps [4]. To describe the photoluminescence (PL) kinetics under the off-resonant pulse excitation of a semiconductor slab, we apply the adiabatic approach to the full exciton-photon-phonon Hamiltonian H H ¼Ĥ H exÀphot þĤ H exÀdisorder þĤ H exÀphon , at first treating quantum-mechanically the exciton-light interactionĤ H exÀphot and structural disorder potential [5]Ĥ H exÀdisorder and then accounting statistically for the exciton-phonon scattering and dephasing due toĤ H exÀphon , since the latter take place on a much larger time scale than the radiative decay time of an individual exciton G À1 . At the same time we assume that due to the optical-phonon-assisted processes hot excitons are quickly dropped (quicker than G À1 ) to the exciton resonance energy where they can be scattered afterwards by acoustic phonons within a small energy window around hw ex . Even though excitons are strongly coupled to the bulk photon