We have investigated ultrathin FexNi1-x films grown epitaxially on Cu(100) with different stochiometry. With the surface magneto-optic Kerr effect (SMOKE) we measured the variation of the Curie temperature T-C as a function of the film thickness n in monolayers (ML). Using the results of our previous investigations on finite-size scaling (Huang et al.), we are able to extrapolate the value T-C(infinity) for samples with different Fe content. In particular, alloy films with Fe concentrations close to 65% remain ferromagnetic. This is in contrast to bulk Fe65Ni35, which shows a collapse of long range order, which is the so-called invar effect associated with a fcc to bcc structural transition. Growing these alloy films on a Cu(100) substrate forces them to adapt the Cu lattice spacing, thereby suppressing the structural relaxation. (C) 1996 American Institute of Physics.