Angle-dispersive x-ray powder diffraction experiments have been performed on neodymium metal to a pressure of 302 GPa. Up to 70 GPa we observe the hP4→cF4→hR24→oI16→hP3 transition sequence reported previously. At 71(2) GPa we find a transition to a phase which has an orthorhombic structure (oF8) with eight atoms in the unit cell, space group Fddd. This structure is the same as that recently observed in samarium above 93 GPa, and is isostructural with high-pressure structures found in the actinides Am, Cf, and Cm. We see a further phase transition at 98(1) GPa to a phase with the orthorhombic α-U (oC4) structure, which remains stable up to 302 GPa, the highest pressure reached in this study. Electronic structure calculations find the same structural sequence, with calculated transition pressures of 66 and 88 GPa, respectively, for the hP3→F8 and oF8→oC4 transitions. The calculations further predict that oC4-Nd loses its magnetism at 100 GPa, in agreement with previous experimental results, and it is the accompanying decrease in enthalpy and volume that results in the transition to this phase. Comparison calculations on the oF8 and oC4 phases of Sm show that they both retain their magnetism to at least 240 GPa, with the result that oC4-Sm is calculated to have the lowest enthalpy over a narrow pressure region near 200 GPa at 0 K.