In a previous paper (Johnson 1974), the notion of state overdescription in dynamical systems was introduced and some general results, applicable to a broad class of nonlinear dynamical systems, were derived. In the present paper those previous general results are applied to the special case of time-invariant linear dynamical systems where several refinements can be made. It is shown that state overdescription, in that case, can be characterized in terms of a simple rank condition for the system matrices. Moreover, that condition leads to a special mode of failure of Kalman's well-known controllability criterion. The latter result is shown to have a somewhat unique interpretation in ‘ transfer functions ‘ pole-zero cancellations ’.