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We discuss the behavior of the two-channel Kondo model with channel anisotropic exchange couplings by using our recent solution of the model. This solution provides an analytic description of the interesting cross-over from a high-temperature regime, dominated by the non-Fermi-liquid behavior of the isotropic two-channel Kondo model, to a low-temperature regime characterized by the standard Fermi-liquid behavior of the single-channel Kondo model.

The Kondo effect in a (quasi-)two-dimensional metal is studied. The special feature of the two-dimensionality is the Van Hove singularity in the electron density of states. For the band filling choosen such, that the Fermi level is close to the saddle points of the band spectrum, the Van Hove singularity comes into play and changes the usual Kondo log to the log2. It turnes out to be possible to carry out the first order parquet summation and to obtain the conditions for the Kondo antiferromagnetic resonance for an arbitrary geometry of the band spectrum. The connection with the Orthogonality Catastrophe is traced and it is shown, that the weak coupling Kondo problem just corresponds to the intermediate asymptotics of the metal's relaxation in a time-dependent external potential.