Conversion-electron Mossbauer spectra of epitaxial alpha'-Fe(1)6N(2) and alpha'-Fe8N films have been studied and their differences are discussed in detail. The Mossbauer spectrum of alpha'-Fe(1)6N(2) can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mossbauer spectrum of alpha'-Fe8N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for alpha'-Fe(1)6N(2) than for alpha'-Fe8N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for alpha'-Fe(1)6N(2). The iron moments tend to locate in the film plane for alpha'-Fe(1)6N(2) and to arrange perpendicularly to the film plane for alpha'-Fe8N.