The main result of this paper states that residual intersections of licci ideals in a local Gorenstein ring \((R,\text{ m})\) are strictly glicci, hence glicci. Unfortunately the proof of this nice result does not carry over to the homogeneous case where only a somewhat weaker result holds. Two proper ideals \(I\) and \(J\) in \(R\) are said to be linked with respect to an ideal \(K\) if \(J= K:I\) and \(I=K:J\); they are \(CI\)-linked (resp. \(G\)-linked) if \(K\) is a complete intersection (resp. Gorenstein) ideal. These notions generate the equivalence relation \(CI\)-liaison (resp. \(G\)-liaison). Then \(I\) licci (resp. glicci) means that \(I\) is in the \(CI\)- (resp. \(G\)-) linkage class of a complete intersection, while strictly glicci means glicci in the ring \(R/(y_1,\dots,y_t)\) for every \(t \geq 0\) and every \(R\)-sequence \(y_1,\dots,y_t\) that is regular on \(R/I\). Moreover if \(I\) is a proper ideal in \(R\) of height \(ht(I)=g\) and \(K\) an ideal minimally generated by \(s \geq g\) elements contained in \(I\), then \(J := K:I\) is called an \(s\)-residual intersection of \(I\) provided \(J\) is a proper ideal of height at least \(s\). A residual intersection \(J\) of a Cohen-Macaulay ideal \(I\) may fail to be unmixed or Cohen-Macaulay, unlike what happens under \(G\)- and \(CI\)-linkage. Indeed \(H_{\text{ m}}^i(R/J)=0\) for \(0 \leq i < \dim R/I\) if \(J\) is \(G\)-linked to \(I\) (see [\textit{P.\ Schenzel}, J.\ Math.\ Kyoto Univ.\ 22 , 485--498, (1982; Zbl 0506.13012)]), and through several theorems one is led to ask whether every Cohen-Macaulay ideal is glicci for \(R\) regular (cf. [\textit{J. O. Kleppe}, Mem. Am. Math. Soc. 732, 116 p. (2001; Zbl 1006.14018)]). Let \(J\) be an \(s\)-residual intersection of \(I\) and let \(y_1,\dots,y_t\), \(t \geq 0\), be an \(R\)-sequence that is regular on \(R/J\). The authors have to prove several theorems to get their main result, e.g. they first need to modify the licci ideal \(I\) within its \(CI\)-linkage class without changing \(J\) such that \(y_1,\dots,y_t\) becomes an \(R/I\)-sequence and so that \(I\) has the property \(G_s\): stating that the number of minimal generators of \(I_p\) is at most \(\dim R_p\) for every prime \(p \in V(I)\) with \(\dim R_p \leq s-1\). Once having the ideal \(I\) with the property \(G_s\) then \(J\) is under some assumptions modified within its even \(G\)-liaison class without changing \(I\), and finally, a sequence of tight double links (called basic double links in geometry) brings \(J\) closer to a complete intersection in such a way that one may conclude by induction on the number of double links of \(I\) leading to a complete intersection. The paper also contains a discussion and give examples showing that the theory of linkage in local rings does not in general pass over to the corresponding theory of homogeneous ideals in projective geometry.