In this article we pursue the problem of equality of Artin factors with those defined on the representation theoretic (analytic) side by the local Langlands correspondence. We propose a set of axioms for the factors on the analytic side which allows us to prove the equality of the factors. In the case of L-functions the equality can be proved in a number of cases appearing in the Langlands-Shahidi method since one of the axioms, stability under highly ramified twists, is already available for the L-functions coming from this method.