Accelerator experiments show that multiple production of hadrons in high-energy collisions of particles involves the formation of unstable intermediate entities, which subsequently decay into the final hadrons. These entities are apparently not only the comparatively light resonances with which we are already familiar but also heavy nonresonant clusters (with a mass above 2--5 GeV). The cluster concept was introduced previously in cosmic-ray physics, under the name "fireballs." To determine what these clusters are from the standpoint of quantum field theory, a detailed and thorough analysis is made of some analogous processes in quantum electrodynamics which are amenable to calculation. The QED analogs of the nonresonant clusters are "half-dressed" electrons and heavy photons. The half-dressed electrons decay into photons and electrons and are completely observable entities, whose interaction properties distinguish them from dressed electrons. In other words, the nonresonant particles are generally off-shell particles (the excursion from the mass shell is in the timelike direction). The assumption that hadron clusters are only resonances would be equivalent to a very specialized assumption regarding the nature of the spectral function of the hadron propagator; it would be different from that in electrodynamics, where the spectral function can be calculated. Nonresonant hadron clusters thus fit naturally into hadron field theory and are nonequilibrium hadrons far from the mass shell in the timelike direction. (In certain cases, their structural distortion is of the same nature as that of a half-dressed electron, so that this term can be conventionally applied to them as well.