  The Kondo effect strongly depends on spin and orbital degrees of freedom of
unconventional superconductivity. We focus on the Kondo effect in the $p_x + i
p_y$-wave and $d_{x^2 - y^2} + i d_{xy}$-wave superconductors to compare the
magnetic properties of the spin-triplet and spin-singlet Cooper pairs. The
difference appears when both of the paired electrons couple to a local spin
directly. For the $p_x + i p_y$-wave, the ground state is always a spin doublet
for a $S_{\rm imp} = 1/2$ local spin, and it is always a spin singlet for
$S_{\rm imp} = 1$. The latter is due to uniaxial spin anisotropy of the triplet
Cooper pair. For the $d_{x^2 - y^2} + i d_{xy}$-wave, the interchange of ground
states occurs, which resembles a competition between the Kondo effect and the
superconducting energy gap in s-wave superconductors. Thus the internal degrees
of freedom of Cooper pairs give a variety to the Kondo effect.
