The magnetic anomalies due to the interaction of the energy levels of a rare-earth ion in a strong magnetic field are studied experimentally and theoretically for the van-Vleck paramagnet PrVO₄. A maximum is discovered in the differential susceptibility dM/dH in a field H _c ≈ 45 T, where the lower energy levels cross. The magnetocaloric effect in pulsed fields is calculated assuming the magnetization process to be adiabatic. This effect is characterized by the absence of initial heating of the sample when the field is turned on and strong cooling as H _c is approached. It is shown that in PrVO₄, which is an enhanced nuclear magnet, the hyperfine interaction plays an extremely important role for the magnetic anomalies associated with crossover. For another van-Vleck paramagnet, HoVO₄, it is shown that a second crossover occurs near 310 T and the magnetocaloric effect is calculated.