Deformation of Residual Intersections

It is shown that in a Cohen-Macaulay local ring, the generic linkage of an ideal $I$ is a deformation of the arbitrary linkage of $I$. This fact does not need $I$ to be a Cohen-Macaulay ideal. The same holds for $s$-residual intersections of $I$ when $s$ does not exceed the height of $I$ by one. Under some slight conditions on $I$, one further generalizes this principle to encompass any $s$-residual intersection.