L1(0)-ordered FeNi, showing high uniaxial magnetic anisotropy (K-u), is promising as a 'rare metal-free' high K-u material. We have worked on L1(0)-ordered FeNi thin films prepared by two methods: one is molecular beam epitaxy (MBE) with alternate deposition of Fe and Ni monatomic layers, and the other is sputtering with co-deposition or multilayer-deposition of Fe and Ni followed by rapid thermal annealing (RTA). For the MBE films prepared by alternate monatomic layer deposition (leading to the stoichiometric composition: Fe 50 at.%-Ni 50 at.%), a clear relationship between K-u and the long-range order parameter S estimated by synchrotron x-ray diffraction (XRD) was found with maximum values of S = 0.48 and K-u = 7.0 x 10(6) erg cm(-3). The composition dependence of K-u was also investigated by deviating the thickness from monatomic layer, showing a maximum of 9.3 x 10(6) erg cm(-3) around 60 at.% Fe. In addition, the effect of Co addition to L1(0)-ordered FeNi was investigated, suggesting that a small amount (< 10 at.%) of Co substitution for Ni would enhance K-u if S keeps the same. The experiments were in qualitatively good agreement with the first-principles calculations. The magnetic damping constant a was also measured to be approximately 0.01 irrespective of S, suggesting that L1(0)-FeNi is a candidate material with high K-u and low a. For the sputtered films with RTA, no major difference between co-deposition and multilayer-deposition was found: in both cases the formation of L1(0)-ordered phase after RTA was definitely confirmed by XRD. Transmission electron microscopy observations indicated that nanometer-sized L1(0)-ordered clusters were dispersed in a disordered phase, in contrast to that of MBE films showing the homogeneous formation of L1(0)-ordered phase. The enhancement of coercivity (H-c) and residual magnetization (M-r/M-s) was observed associated with the appearance of L1(0)-ordered phase. The maxima of H-c and M-r/M-s were obtained to be 1.35 kOe and 0.22, respectively.