Cross sectional and plane-view transmission electron microscopy (X- and PV-TEM) were used to investigate the initial growth phase of 5, 10, 20 and 40 nm thick Ni1-xFex (x = 0.6-0.8) films, prepared on MgO(001) covered with a buffer layer of Fe or Ni as well as on naked MgO(0001). The 100 nm thick buffer layers of Fe and Ni were pre-grown on MgO(001). All of Ni0.20Fe0.80, Nio(0.40)Fe(0.60), Fe and Ni films could be epitaxially grown at 250 degreesC by de-biased plasma sputtering at 2.9 kV in pure Ar gas. The films of Ni0.20Fe0.80 and Ni0.40Fe0.60 were grown in their own stable phase, bce and fee on MgO(001), respectively. However, Ni0.20Fe0.80 film could be grown in fee phase pseudomorphic with Ni(001) up to 20 nm thick on Ni/MgO(001), while Ni0.40Fe0.60 film in bce phase pseudomorphic with Fe(001) up to 10 nm thick on Fe/MgO(001). With increasing thickness, their growth phases transformed into their own stable phases. Whether or not the pseudomorphic phase may be induced and what its critical thickness may be should depend primarily on the lattice misfit between the crystal planes in contact. The growth mode of Ni0.40Fe0.60 film was investigated more in details to be compared with the simulations of the average strain energy versus thickness and with those of the critical thickness of the pseudomorphic films versus the lattice misfit between the contacted crystal planes.