The theory of the asymptotic behaviour of the root-loci of linear, time-invariant, multivariable, feedback systems is developed. It is shown that each of the system zeros attracts, and is a terminating point of, one of the root-loci, as the feedback gain tends to infinity. The root-loci, that are not attracted by the zeros, tend to infinity in a special pattern that is dictated by the eigen-properties of the elementary matrices of the system. To complete the geometric description of the asymptotic behaviour of the root-loci, the concept of infinite zeros and their order is introduced. Each infinite zero of orderrattracts one root-locus and, together withr−1 other infinite zeros of the same order, the corresponding asymptotes form a Butterworth configuration of orderraround a special point defined as a ‘ pivot ’.