The oxide Ba4Ca0.9Mn3.1O11.3 is closely related to the hexagonal perovskite family, and its fine structure is studied by high-resolution electron microscopy. Different structure models are proposed and discussed. The image contrast is best explained assuming a displacement of two manganese atoms with regard to the ideal 16L octahedral configuration. These displacements are directly related to the existence of tetrahedral layers. Ba4Ca0.9Mn3.1O11.3 can then be described as a sequence along (c) over right arrow of an hexagonal stacking (h) of BaO3 layers, a cubic close-packed stacking (c) of BaO3 layers and a cubic stacking (c ') involving oxygen deficient BaO2 layers, according to the sequence (hhhccc ' cc)(2). Small amounts of Cu can be introduced into the 16L Ba-Ca-Mn-O structure without any influence on the microstructure. The stacking sequence is similar to the one observed for pure Ba4Ca0.9Mn3.1O11.3. No defects and/or violations of the stacking sequence are observed.