Cross-sections for elastic scattering of muonic hydrogen on helium nuclei, (hµ) 1s + He ++ , where h and He ++ stands for a hydrogen and a helium isotope nucleus, respectively, were calculated in the one-level adiabatic approximation for a range of collision energies from 0 to 50 eV. Bound states and energy levels of (hµHe) ++ molecular ions were also calculated and compared with their Born-Oppenheimer counterparts. It is shown that adiabatic corrections are responsible for proper positions of the RamsauerTownsend minima in (hµ)1s + He ++ elastic scattering and, at the same time, they significantly influence bound states and energy levels of (Heµh) ++ and (Heπh) ++ ions. Calculations were performed in the frame of the phase--function method.