This paper is concerned with the qualitative behaviour of the multivariable root-locus for high and low gains. For a non-singularm×mrational transfer function, the Butterworth approach and departure patterns are shown to be determined in all cases by the zeros and poles of certain algebraic functions. These are in turn characterized (at each point of the extended complex plane) by a set ofmrational numbers called the root-locus indices. In addition, the Smith-McMillan pole-zero structure of the transfer function is represented (at each point of the extended complex plane) by a sequence ofmintegers, called the McMillan indices. An algebraic condition for the coincidence of the two sets of indices is established using the algebraic function theory underlying the Newton diagram method together with a valuation characterization of the Smith-McMillan form. It is shown directly (without simple null structure assumptions or equivalent conditions on constant matrices) that the condition is generically met. The analysis also establishes a close link with the existing algebraic function approach to the generalized Nyquist stability criterion where the relationship between the two types of poles and zeros is of crucial importance. The case of a rank deficient transfer function is briefly considered.