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The ratio of the plasma pressure to the magnetic field pressure (or the ratio of their energy densities)-plasma parameter “beta” (β)-is critical in determining the dynamics of the interaction of the solar wind with planetary magnetospheres and has important implications to the propagation of energetic particles and to the structure of the shocks. In the interplanetary space, the value of “beta” is usually in the range of 0.1-1.0, and the contribution of the superthermal particles to the plasma pressure is generally assumed negligible. However, the analysis of energetic particles and magnetic field measurements by the Ulysses spacecraft shows that, in a series of events, the energy density contained in the superthermal tail of the particle distribution is comparable to or even higher than the one of the magnetic field, creating conditions of high-beta plasma. In this paper, we extensively survey and analyze measurements of the energy density ratio (parameter ) of the energetic particles (20 keV-5 MeV) to the magnetic fields by Ulysses, for its entire trajectory (1990-2009), in order to find occurrences of high-beta (βep >; 1) superthermal plasma conditions. As expected, periods of dominant magnetic energy were observed most of the time, for the above mentioned particle energy range. Nevertheless, a number of 484 distinct periods with a total duration of 406.02 days were identified when the energy density carried by the energetic ions overwhelmingly dominated that of the magnetic field. These interplanetary high-beta (βep >; 1) events are characterized by a very high parameter (up to ~1733), a great total duration (of 406.02 days), and a large percentage (11.3%) of the total mission lifetime (in presence of energetic particle events). Furthermore, these events were detected within well-identified regions corresponding mainly to the following: 1) the vicinity of shock fronts; 2) the v- - icinity of large transient disturbances associated with shock waves; 3) filamentary magnetic structures; and 4) the vicinity of the Jovian magnetospheric environment. These events were also associated with energetic particle intensity enhancements due to the following: 1) reacceleration at interplanetary corotating interaction regions (CIRs), solar flare (blast), transient, and/or CME-driven shocks; 2) unusually large magnetic field depressions; 3) Jupiter's bow shock particle acceleration; and 4) leakage from Jupiter's magnetosphere.