The epsilon Fe2O3 phase of iron oxide has been studied to understand the spin structure and the magnetocrystalline anisotropy in the bulk and in thin films of ε-Fe2O3 and Co-doped ε-Fe2O3. The preferential magnetization direction in the nanoparticles of ε-Fe2O3 is along the a-axis [M. Gich et al., Chem. Mater. 18, 3889 (2006)]. Compared to the bulk band gap of 1.9 eV, the thin-film band gap is reduced to 1.3 eV in the Co-free films and to 0.7 eV in the film with partial Co substitution. The easy magnetization direction of the bulk and Co-free ε-Fe2O3 is along the a-axis, but it switches to the a-axis on Co substitution. All three systems exhibit in-plane anisotropies associated with the orthorhombic crystal structure of the oxide