The conductance and the current of spherical quantum dots ͑SQD's͒ containing a small number of electrons are studied as a function of source-drain and gate voltages. The influences of magnetic field, spatial symmetry, electron-phonon interaction, dot radius, and temperature on the transport properties are analyzed. The manyparticle states of the SQD's are described by the total spin ͑S͒ and total orbital ͑L͒ angular momenta (LS-coupling scheme͒ within the Hartree-Fock approximation, where the electron-electron interaction is included via a multipole expansion. The tunneling current is obtained by solving the master equation for the occupation number of the many-particle states of the system. The appearance of a negative differential conductance, due to the orbital-blockade mechanism directly related to the spherical central potential of the quantum dot, is reported.In order to obtain the transport properties we will follow the same formalism described in Ref. 2 for one-dimensional systems. We consider a double barrier system formed by two