We propose a model that we believe is the main source of the antihyperon polarization in high-energy protonnucleus inclusive reactions. The polarization is originated by the final-state interactions between the antihyperons and other produced particles in these collisions (predominantly pions). The model is based on two elements: the low-energy pion-hyperon interaction (described by chiral effective Lagrangians) and the statistical fluctuations plus expansion of the background matter.In 1976, Bunce and collaborators [1], studying the Λ inclusive productionwith 200 GeV protons, where X represents the not observed particles, verified that the Λ polarization was significantly different from zero (and negative, reaching values close to 20%). These results were totally unexpected [2], because there were indications that polarization effects should vanish at high energies and hadron polarization was believed to be a low energy phenomenon. Since then, many similar experiments have been performed [3]- [6], that confirmed these results and have shown also that both hyperons and antihyperons produced are polarized in this kind of reaction. However, the variety of behavior of the polarizations has caused many problems to the theoretical understanding of the experimental data ([7]-[9] for example), specially in the antihyperon case. Since these models are based in direct mechanisms for hyperon production (the initial proton becomes a hyperon, by some mechanism, such as quark recombination [7], for example) the final antihyperon polarization practically vanishes.The first model that was able to produce polarized antihyperons, was the one proposed by Y. Hama and T. Kodama [10] and it was based in the hydrodynamical model. The hyperon is produced inside a medium composed of hot hadronic matter (produced in the collision process) and interacts with it. This interaction was represented by an optic potential. With this model, the antihyperon data were quite well reproduced. Nevertheless, the model left some questions in open, such as the need of different potentials for different hyperons and their interpretations.Aiming to study these questions, a new model was developed, [11], based in [10]. The hyperon was considered to be produced unpolarized (as an average effect) in the interior of a hot hadronic matter, now considered as a fluid composed of particles (predominantly pions). The hyperon (or antihyperon) interacts with the other hadrons (instead of considering a potential as it was done in [10]), and becomes polarized due to these final state interactions. The remainder of this work will be devoted to the presentation of the main features of this model, and the results of the Λ and Ξ + polarizations (the calculations to the Σ − polarization are in progress). To build a model with the cited characteristics, two elements must be considered: the microscopic interactions, that happen inside the hadronic matter, and the calculation of averages, considering the fluid in expansion. A brief description of these elements will be ma...