  We investigate the low-temperature dynamics of single electron boxes and
transistors close to their degeneracy point using renormalization group
methods. We show that intermode scattering is a relevant perturbation and
always drives the system to the two-channel Kondo fixed point, where the two
channels correspond to the real spins of the conduction electrons. However, the
crossover temperature T^*, below which Matveev's two-channel Kondo scenario
[K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentially
with the number of conduction modes in the tunneling junctions and is extremely
small in most cases. Above T^* the 'infinite channel model' of
Ref.{onlinecite{Schoen}} turns out to be a rather good approximation. We
discuss the experimental limitations and suggest a new experimental setup to
observe the multichannel Kondo behavior.
