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Pickup protons are produced as a result of ionization of interstellar hydrogen on the solar wind protons. Immediately after their birth pickup protons start to suffer influence of the frozen-in solar wind magnetic field, initially following helical trajectories about the local field. Interaction with magnetic solar wind fluctuations results in isotropization of their distribution in the solar wind reference frame and also, in energy diffusion, which operates sufficiently slower. Adiabatic deceleration on radially expanding solar wind results in evolution of initially isotropic velocity distribution to a spherical one – a typical “plateau” appears in the low part of the spectrum, and energy diffusion leads to formation of high-energetic “tail”, i.e. the specific population of protons with velocities two or more times greater than that of solar wind. Theoretical study of distribution of pickup ions in the heliosphere and of acceleration processes there had been taken earlier, (see Chalov, 2008, Isenberg, 1987, Vasyliunas & Siscoe, 1976 and others), but most of them did not take the time evolution of solar wind into account. However, this effect, connected, in particular, with the solar cycle, leads to propagation of shock waves in the inner heliosheath, where solar wind is subsonic. In the regions with large density gradients sufficient adiabatic heating of frozen-in pickup protons may occur. Perhaps, these “warmed” protons may notably contribute into so-called “suprathermal” component of the spectrum, measured “in situ” on Voyager spacecrafts and remotely by IBEX. In present work we study how non-stationary solar wind effects influence the energy distribution of pickup protons in the inner heliosheath.