  We study the Kondo effect in a single quantum dot system with two or three
orbitals by using the Bethe-ansatz exact solution at zero temperature and the
non-crossing approximation at finite temperatures. For the two-orbital Kondo
effect, the conductance is shown to be constant at absolute zero in any
magnetic fields, but decrease monotonically with increasing fields at finite
temperatures. In the case with more orbitals, the conductance increases at
absolute zero, while it features a maximum structure as a function of the
magnetic field at finite temperatures. We discuss how these characteristic
transport properties come from the multi orbital Kondo effect in magnetic
fields.
