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Ni-Cu films display an "unusual" reorientation as a function of thickness, where the magnetization rotates from an in-plane to an out-of-plane orientation upon increase of the thickness. On the other hand, Fe-Cu films show an "usual" reorientation transition where the magnetization rotates from a an out-of-plane to an in-plane orientation if the thickness is increased. We have studied the crossover between the different reorientation behavior by preparing FexNi1-x-Cu alloys in ultrahigh vacuum (UHV) and studied the magnetic properties with in situ magneto-optic Kerr effect (MOKE). For Ni-rich alloy films, we find that the critical thickness dc ("unusual transition") is a very sensitive function of the alloy concentration. Starting with dc = 8.5 ML for Ni-Cu, we obtained a value of dc ∼ 20 ML for Fe5.6M94.4. These results can be explained on the basis of elastic and magnetoelastic properties of bulk FexNi1-x alloys. Beyond this Fe concentration, we could not observe any reorientation, the magnetization stayed in the plane. At ∼ 35% Fe we could observe an "usual" transition at ∼ 1.9 ML for a sample temperature of 110 K. This value increased to ∼ 3 ML for Fe72Ni28, beyond this concentration, we could observe "magnetic live surface layers.".