A unified approach to input-output decoupling of linear multivariate control systems described by dynamic operator equations is presented. The motivation of the approach is to include as special cases all linear decoupling results presently known and to cover some new cases not previously studied. The generality of the results is due to three facts: first to the inclusion of a direct input-output effect in the system model, secondly to the utilization of operator theory concepts and thirdly to the treatment of the case where the decoupling matrix operator B* is singular by means of dynamic compensation. Several examples illustrate the generality of the present theory and give some now situations whore input-output decoupling is of importance