  The multichannel Kondo model with SU(N) spin symmetry and SU(K) channel
symmetry is considered. The impurity spin is chosen to transform as an
antisymmetric representation of SU(N), corresponding to a fixed number of
Abrikosov fermions $\sum_{\alpha}f_{\alpha}^{\dagger}f_{\alpha}=Q$. For more
than one channel (K>1), and all values of N and Q, the model displays non-Fermi
behaviour associated with the overscreening of the impurity spin. Universal
low-temperature thermodynamic and transport properties of this non-Fermi liquid
state are computed using conformal field theory methods. A large-N limit of the
model is then considered, in which K/N and Q/N are held fixed. Spectral
densities satisfy coupled integral equations in this limit, corresponding to a
(time-dependent) saddle-point. A low frequency, low-temperature analysis of
these equations reveals universal scaling properties in the variable
$\omega/T$, also predicted from conformal invariance. The universal scaling
form is obtained analytically and used to compute the low-temperature universal
properties of the model in the large-N limit, such as the T=0 residual entropy
and residual resistivity, and the critical exponents associated with the
specific heat and susceptibility. The connections with the ``non-crossing
approximation'' and the previous work of Cox and Ruckenstein are discussed.
