Nuclear decays into three-particle channels are considered in a few-body approach of hyperspherical harmonics with emphasis on simultaneous, or direct, emission of two protons. General conditions of direct decays are described and their main features, being experimentally established in decays of light nuclei, are reported. The analysis method based on an expansion of decay amplitude into a series of hyperspherical harmonics is reviewed. This basis is a generalisation of the spherical function basis in three-body systems. The method is tested on analysis of the direct decay6Be→&agr;+p+pwhere the three-body components in the nuclear structure of6Behave been studied. In particular, the observed strong proton-proton correlations are treated as a manifestation of a specific three-body quantum effect: the kinematic focusing of fragments over momenta and in space. The method is applied for the predictions of proton-proton correlations and life-time estimates of the nuclei19Mg,34Caand48Ni-candidates for two-proton radioactivity. Each direct 2p-decay should result in a set of peaks in theEp−pspectrum whose number and positions depend on the structure of initial nucleus, opposite to the diproton model, predicting the2Heemission with one peak atEp−p≈0in all cases. ©2000 American Institute of Physics.