  We study magnetoconductance of the small bandgap carbon nanotube quantum dots
in the presence of spin-orbit coupling in the strong correlations regime. The
finite-U mean field slave boson approach is used to study many-body effects.
Different degeneracies are restored in magnetic field and Kondo effects of
different symmetries arise including SU(3) effects of different types. Full
spin-orbital degeneracy might be recovered for zero field and correspondingly
SU(4) Kondo effect sets in. We point out on the possibility of the occurrence
of electron-hole Kondo effects in slanting magnetic fields, which we predict
will occur in the available magnetic fields for orientation of fields close to
perpendicular. When the field approaches transverse orientation a crossover
from SU(2) or SU(3) symmetry into SU(4) is observed.
