Expected evolution of the fluxes of the H and He components of the Neutral Solar Wind (NSW) during the solar cycle is discussed. A newly-developed, time-dependent model takes into account the typical solar cycle-related variations of the ionization rates as well as modulations of the neutral gas distribution which affect the NSW production in the interplanetary space. The distribution of the NSW flux is analyzed with respect to the heliocentric distance from the Sun and the angle from the interstellar wind apex. It demonstrates strong, time-dependent, spatially anticorrelated upwind-to-downwind asymmetries of the neutral H and He fluxes in the solar wind. The most pronounced modulation of the NSW is expected around the solar maximum epoch along the downwind axis, where a strong decrease of the hydrogen flux (by up to two orders of magnitude at ∼1 AU) is predicted. The helium component exceeds the hydrogen one in the downwind region up to distances of ∼2–4 AU (depending on the phase of the solar cycle), wh...