  We reinvestigate the two channel flavor anisotropic model (2CFAK) and one
channel compacitified Kondo model (1CCK). For these two models, all the
possible fixed points and their symmetries are identified; the finite size
spectra, the electron conductivity and pairing susceptibility are calculated.
It is shown that the only non-fermi liquid (NFL) fixed point of the 2CFAK is
the NFL of the two channel Kondo model (2CK) with the symmetry $O(3) \times
O(5)$. Any flavor anisotropies between the two channels drive the system to the
fermi-liquid (FL) fixed point with the symmetry $O(4) \times O(4)$ where one of
the two channels suffers the phase shift \pi/2 and the other remains free. The
NFL fixed point of the 1CCK has the symmetry $O(3) \times O(1)$ and has the
same thermodynamics as the NFL fixed point of the 2CK. However, in contrast to
the 2CK, its conductivity shows $T^{2}$ behavior and there is no pairing
susceptibility divergence. Any anisotropies between the spin and isospin
sectors drive the system to the FL fixed point with the symmetry O(4) where the
electrons suffer the phase shift \pi/2. The connection and differences between
the two models are explicitly demonstrated. The recent conjectures and claims
on the NFL behaviors of the two models are commented.
