The crystal structures of alpha-NF3 and beta-NF3 are reported for the first time. As shown by powder neutron diffraction, the low-temperature alpha-NF3 crystallizes in the orthorhombic space group Pnma (oP16) with lattice parameters a = 6.71457(13) angstrom, b = 7.30913(14) angstrom, c = 4.55189(8) angstrom, V = 223.396(7) angstrom(3), and Z = 4 at T = 6 K. The intramolecular atom distances in alpha-NF3 are 1.3639(16) and 1.3677(11) angstrom for N-F, and 2.1216(16) and 2.120(2) angstrom for F ...F. The F-N-F bond angles are 101.92(7)degrees and 101.63(10)degrees. All data are in excellent agreement with quantum-chemical predictions and previously reported experimentally obtained gas-phase data. The high-temperature beta-NF3 is a plastic crystal, space group P4(2)/mnm (tP120), with the lattice parameters a = 15.334(6) angstrom, c = 7.820(3) angstrom, V = 1838.6(12) angstrom(3), and Z = 30 at T = 60 K. Its crystal structure is closely related to that of the Frank-Kasper sigma phase.