We conclude our investigation (started in Part 1 : Goodwin and Fletcher 1995) of the problem of pole assignment by real output feedback in descriptor systems. Sufficient conditions are given for the existence of a real feedback matrix which exactly assigns an almost arbitrary set of r (the number of semi-state variables of the system) distinct numbers to the closed-loop generalized eigenspectrum of the system. It is further shown that where exact assignment may not be possible we can at least approximately assign the set. This agrees with work of other authors (see, for example, Ailon 1991). The sufficient conditions combine with results from Part 1 to give criteria for pole assignment. Furthermore, the inductive nature of the proof in this paper (and also in Part 1) gives rise to an algorithm for calculating the desired feedback when it exists.