A comparative analysis of the features of UV- stimulated emission (SE) of various types of disorder active materials based on ZnO crystallites for a random laser (RL) was carried out. The superlinear increase in the intensity of the UV photoluminescence (PL) band of polydisperse nano- microcrystalline (PNMC) ZnO powder at a wavelength of λ = 387 nm and some narrowing of its half-width in the range of 20-15 nm with increasing pump intensity indicate random lasing with incoherent feedback (FB). Properties of similar UV PL bands under the same conditions from a thin film containing hexagonal ZnO microdisks, as well as samples of monodisperse ZnO nanopowder indicate stimulated emission with coherent feedback. It is shown that, among the studied materials, the PNMC ZnO powder with crystallites contained nano-grains with is the most suitable for creating a laser with incoherent feedback at room temperature. The dominant factor of UV SE in PNMC ZnO powder is radiation transitions under exciton - exciton scattering conditions. The possible mechanisms of this random emission with the continuous spectrum are discussed. The average optical gain coefficient αg at λ = 387 nm in this RL system is estimated, as αg ~ 150 cm-1.