Inelasticity distributions in high-energy p-nucleus collisions are computed in the framework of the interacting gluon model, with the impact-parameter fluctuation included. A proper account of the peripheral events by this fluctuation has shown to be vital for the overall agreement with several reported data. The energy dependence is found to be weak. [S0031-9007(97) PACS numbers: 13.85. Hd, 12.40.Ee, 24.85. + p, 25.40.Ve Inelasticity, i.e., the fraction of the incident energy E 0 which is transformed into produced particles, is one of the basic quantities in high-energy hadronic and nuclear collisions. It is crucial in cosmic-ray data analysis where the primary mass composition, which is an important piece of information about the Universe, is deduced by using cascade models of the development of the mass composition with appropriate inelasticity distributions [1] and cross sections as the inputs. So, it is natural that since early times the study of the inelasticity has received special attention by both experimentalists and theoreticians. More recently, it has also aroused interest in connection with the production of a quark-gluon plasma in heavy-ion collisions [2][3][4][5][6][7]. Yet, experimental data are rather scarce and the theoretical understanding of several aspects of the inelasticity, such as its distribution and E 0 dependence, is far from being satisfactory. The main obstacle in accelerator studies, especially with colliding beams, is the increasing difficulty in detecting those particles which carry the main fraction of E 0 as E 0 increases. As for the models, they are largely in conflict with each other even in explaining such a simple aspect as the E 0 dependence of the inelasticity.A classical model of multiparticle production, which is still popular, is the hydrodynamic model [8]. In any variant of it, the concept of inelasticity is essential, because it defines one of the ingredients, namely, the available energy for particle production. To other types of models, it is just one more variable, which can be computed, without playing a vital role.One of the main features of high-energy hadronic or nuclear collisions is the large event-by-event fluctuation, exhibited in several observed quantities. Thus, in a given experimental setup and even under the same initial conditions for the colliding objects, events with different finalstate configurations occur. For example, inpp collisions at p s 540 GeV [9], the number of charged particles produced in an event varies from 2 to more than 100. It was also reported [10] that, in the CERN intersecting storage ring (ISR), the so-called leading particles, those which carry the largest momentum in the center of mass frame in either direction, are uncorrelated and their momentum distribution is more or less uniform. This implies, in turn, that also the inelasticity varies from event to event. Such fluctuations have either a quantum mechanical or a statistical origin, or even simply associated with the impact parameter. The interacting gluon model (IGM) ...