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Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback inlinear time-invariant descriptor systems are presented. These generalise in a natural way the known corresponding results for state-space systems. However, our arguments extend somewhat existing work on eigenstructure assignment by state feedback in descriptor systems. The main issue throughout the paper is closed-loop regularity, i.e. uniqueness of solutions of the initial value problem, which cannot be taken for granted.