The structural properties of sodium manganates and iron substituted sodium manganates with compositions Na2/3Mn1-xFexO2 (x=0, 1/3 and 2/3) were studied by Raman spectroscopy. The Raman spectroscopy allows distinguishing between layered phases with orthorhombic (Cmcm space group) and hexagonal (P63/mmc space group) distortion. It has been found that the crystal structure and the composition of Na2/3MnO2 display a strong dependence on the history of the thermal treatment. The orthorhombic distorted modification is stabilized at high temperatures (1000 oC). At lower quenching temperature, there is a phase separation into an orthorhombic and a hexagonal modification, concomitant with an increase in the oxidation state of Mn. When Fe substitutes for Mn, the hexagonal modification is stabilized. In order to understand the origin of the Raman spectra of Na2/3Mn1-xFexO2, we have used Na2/3Co2/3Mn1/3O2 as a standard for hexagonal structure, where Co3+ and Mn4+ are statistically distributed in the transition metal layers.