  We study the structural properties of colored Kauffman homologies of knots.
Quadruple-gradings play an essential role in revealing the differential
structure of colored Kauffman homology. Using the differential structure, the
Kauffman homologies carrying the symmetric tensor products of the vector
representation for the trefoil and the figure-eight are determined. In
addition, making use of relations from representation theory, we also obtain
the HOMFLY homologies colored by rectangular Young tableaux with two rows for
these knots. Furthermore, the notion of super-A-polynomials is extended in
order to encompass two-parameter deformations of PSL(2,C) character varieties.
