High-pressure synthesized quasi-one-dimensional NaMn 2 O 4 and Li 0.92 Mn 2 O 4 are both antiferromagnetic insulators. Here their atomic and magnetic structures are investigated using neutron powder diffraction. The present crystal structural analyses of NaMn 2 O 4 reveal that a Mn 3+ /Mn 4+ charge-ordering state exists even at low temperature (down to 1.5 K). It is evident that one of the Mn sites shows a strongly distorted Mn 3+ octahedron due to the Jahn-Teller effect. Above T N = 35 K, a two-dimensional short-range correlation is observed, as indicated by asymmetric diffuse scattering. Below T N , two antiferromagnetic transitions are observed: (i) a commensurate long-range Mn 3+ spin ordering below T N1 = 35 K and (ii) an incommensurate Mn 4+ spin ordering below T N2 = 11 K. Surprisingly, the two antiferromagnetic orders are found to be independent of each other. The commensurate magnetic structure (k C = 0.5, 0.5, 0.5) follows the magnetic anisotropy of the local easy axes of Mn 3+ , while the incommensurate Mn 4+ one shows a spin-density-wave or a cycloidal order with k IC = (0, 0, 0.216). For Li 0.92 Mn 2 O 4 , on the other hand, the absence of a long-range spin-ordered state is confirmed down to 1.5 K.