  We study the Toulouse limit of the multi-channel Kondo model defined as the
limit of maximal anisotropy which can be achieved without changing the infrared
behaviour of the model. It is shown that when the number of channels exceeds 2,
the interactions do not vanish and the Toulouse limit remains a non-trivial
field theory. Considerable simplifications take place only for k = 2, where the
Bethe ansatz reproduces the results by Emery and Kivelson.
