  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.
