Ongoing search for room-temperature superconductivity is inspired by the unique properties of the electron-phonon interaction in metal superhydrides. Encouraged by the recently found highest-T-C superconductor fcc-LaH10, here we discover several superhydrides of another lanthanoid, neodymium. We identify three novel metallic Nd-H phases at pressures ranging from 85 to 135 GPa: I4/mmm-NdH4, C2/c-NdH7 , and P6(3)/mmc-NdH9, synthesized by laser-heating metal samples in NH3BH3 media for in situ generation of hydrogen. A lower trihydride Fm (3) over barm-NdH3 is found at pressures from 2 to 52 GPa. I4/mmm-NdH4 and C2/c-NdH7 are stable from 135 to 85 GPa, and P6(3) /mmc-NdH9 is stable from 110 to 130 GPa. Measurements of the electrical resistance of NdH9 demonstrate a possible superconducting transition at similar to 4.5 K in P6(3)/mmc-NdH9. Our theoretical calculations predict that all of the neodymium hydrides have antiferromagnetic order at pressures below 150 GPa and represent one of the first discovered examples of strongly correlated superhydrides with large exchange spin-splitting in the electronic band structure (>450 meV). The critical Neel temperatures for new neodymium hydrides are estimated using the mean-field approximation to be about 4 K (NdH4), 251 K (NdH7), and 136 K (NdH9).