  The ambiguities inherent in renormalization are considered when using
mass-independent renormalization in massless theories that involve two coupling
coupling constants. We review how there is no renormalization scheme in which
the beta-functions can be chosen to vanish beyond a certain order in
perturbation theory, but that the beta-functions always contain ambiguities
beyond first order. We examine how the coupling constants depend on the
coefficients of the beta-function beyond one loop order. A way of
characterizing renormalization schemes that doesn't use coefficients of the
beta-function is considered for models with either one or two couplings. The
renormalization scheme ambiguities of physical quantities computed to finite
order in perturbation theory are also examined. We demonstrate how summation of
the logarithms that have explicit dependence on the renormalization scale
parameter mu in a physical quantity R leads to a cancellation with the implicit
dependence of R on mu through the running couplings. It is also shown that
there exists a renormalization scheme in which all radiative effects beyond
lowest order are incorporated into the behaviour of the running couplings.
