The O(3) symmetric Anderson model has a Fermi liquid or marginal Fermi liquid low-energy fixed point, dependent on the parameter V(0), the hybridization matrix element to a local Majorana fermion mode. We use the numerical renormalization group method to calculate the spectral densities. For V(0) = 0 (non-Fermi-liquid case) there is a zero mode in the one-particle spectrum with a weight which decreases exponentially with U for large U. The scattering with this zero mode induces a \omega\ low energy behavior in the single-particle response functions and a In lot divergence in the dynamic spin susceptibility. (C) 1999 Elsevier Science B.V. All rights reserved.