The ambiguities inherent in renormalization are considered when using mass independent renormalization in massless theories that involve two coupling constants. We review how unlike models in which there is just one coupling constant there is no renormalization scheme in which the β-functions can be chosen to vanish beyond a certain order in perturbation theory, and also the β-functions always contain ambiguities beyond first order. We examine how the coupling constants depend on the coefficients of the β-functions beyond one loop order. A way of characterizing renormalization schemes that doesn't use coefficients of the β-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. The renormalization group equation makes it possible to sum the logarithms that have explicit dependence on the renormalization scale parameter μ in a physical quantity R and this leads to a cancellation with the implicit dependence of R on μ through the running couplings, thereby removing the ambiguity associated with the renormalization scale parameter μ. It is also shown that there exists a renormalization scheme in which all radiative contributions beyond lowest order to R are incorporated into the behavior of the running couplings and the perturbative expansion for R is a finite series.