  Following the recent work by Chan, and by Morton and Hadji on the Homflypt
polynomials of some generalized Hopf links, we investigate the Kauffman
polynomials of generalized Hopf links. By studying the Kauffman skein module of
the solid torus S^1\times D^2, we establish a similar skein map on the Kauffman
skein module of S^1\times D^2 which has distinct eigenvalues. Furthermore we
are able to calculate the Kauffman polynomials of some specific generalized
Hopf links.
