This paper describes the relationship between the damping constant and saturation magnetostriction of Ni-Fe M (M Ga, Ag, Mo, and W; 0 0.10) films to clarify the effect of doping elements on and other magnetic properties in these films. For M Ga and Ag, the change of with is closely related with that of , while it is not consistent with that of when M Mo and W. These results suggest that both and are correlated with each other as the single fcc Ni-Fe phase remains unchanged with for M Ag and Ga, while that and are independent from each other because of coexistence of fcc Ni-Fe and new phases when M Mo and W. Therefore, it is pointed out that can be controlled effectively by selecting the doping elements which do not induce a new phase in the Ni-Fe binary alloy, but one should be careful about a change in magnetoelastic properties which may deteriorate magnetic softness. These results for M Ga and Ag also suggests that Ni-Fe M films are good examples to give evidence that the magnetoelastic energy has the same intrinsic origin with .