  We report on the progress in the computation of the beta-functions of phi^4
theory and QCD in the large N expansion. For the former we give an analytic
formula for the critical exponent which encodes higher order coefficients in
the series beyond those currently known in the MSbar scheme at O(1/N^2) in a
large N expansion. This allows us to deduce new coefficients in the field
anomalous dimension which relate to Kreimer's knot theory of the divergences of
a quantum field theory. A similar exponent is computed for the beta-function of
QCD at O(1/N_f).
