© 2018 American Physical Society. An analysis is presented of the Np237-O17 cross-relaxation (CR) process at temperatures below T=10 K that was reported [Tokunaga, Phys. Rev. B 74, 064421 (2006)10.1103/PhysRevB.74.064421] in O17 NMR studies of NpO2. The CR evidently results from Np237 spin fluctuations driven by indirect spin-spin interactions analogous to the Suhl-Nakamura [Nakamura, Prog. Theor. Phys. 20, 542 (1958)10.1143/PTP.20.542] effect in conventional magnets. Here, however, there is a body of evidence that the interacting Np4+ ions are in a magnetic, rank-5 dotriakontadipolar ground state [Santini, Phys. Rev. Lett. 97, 207203 (2006)10.1103/PhysRevLett.97.207203; Magnani, Phys. Rev. B 78, 104425 (2008)10.1103/PhysRevB.78.104425]. Owing to the observed exponential form of the fluctuation spectrum, it is possible to evaluate explicitly the CR bandwidth in terms of any specified Np237-Np237 (spin-spin) coupling Hamiltonian. We model the latter as an enhanced dipolar coupling. The enhancement is concluded to be compound, with the "enlarged nuclear moment" mechanism identified in the paramagnetic state [Tokunaga, Phys. Rev. B 74, 064421 (2006)PRBMDO1098-012110.1103/PhysRevB.74.064421] responsible for a factor ∼22, while the indirect Np237-Np237 coupling effect is found to be ∼240 times the amplitude of the classical dipolar interaction. We suggest that these results are consistent with the identification of a magnetic rank 5 multipolar ground state [Magnani, Phys. Rev. B 78, 104425 (2008)10.1103/PhysRevB.78.104425] for NpO2.