The infra-red renormalization properties of the O(N) model is studied to tw
o loops. The calculation is done within a mass dependent renormalization sc
heme. The mass-dependent one-loop renormalization group coefficients are ob
tained and the two-loop coefficients are calculated in the infrared limit.
We observe cancellations within the framework of field theory which make th
e two-loop beta-function coincide with the one-loop beta-function in the in
fra-red limit.