Frequency-domain pole assignment and exact model-matching for delay systems are considered, with the knowledge that the delay plant is not necessarily stable. As for pole assignment for the delay plant, the state-space approach, which is also called the ‘time-domain approach’, is already known. The frequency-domain approach, which is much more fruitful than the time-domain approach, has not previously been developed, and is solved in this paper. As for exact model-matching, which is not only of a higher level but is also a more agreeable design method, neither the time-domain nor the frequency-domain approach has been reported. A newly developed frequency-domain exact model-matching approach is presented in this paper.