Using the numerical renormalization group method, we study a generaliz
ed two-channel Kondo model where the impurity has a quadrupole moment
(pseudospin) and a magnetic moment(flavor). This model may be of relev
ance to the Ce ions in CeB6 and the Cu ions in cuprate superconductors
. We find that the nontrivial fixed point of the two-channel Kondo mod
el is unstable against flavor exchange coupling. The system flows to a
non-Fermi-liquid fixed line. In the presence of a double tenser inter
action, which breaks particle-hole symmetry, the system flows to a Fer
mi-liquid fixed line.