In 1956 Dahlquist showed that stable linear k-step methods cannot exceed a certain consistency order. In 1971 Donelson and Hansen introduced cyclic methods which violate this restriction. Ansorge and Taubert showed that strongly-stable cyclic methods can be applied to smooth as well as non-smooth problems, where the question of order is not important. The question of higher order of the cyclic strongly-stable methods for smooth problems is studied. First of all consistency conditions for m cyclic k-step methods in general for arbitrary order q≥1are algebraically formulated and then 4 cyclic 4-step strongly stable methods of order 5 are constructed. Some numerical test cases are given. The results of these tests show unfavourable rounds off-error propagation. This unfavourable behaviour is then studied. As a result it seems that explicit 4 cyclic 4-step methods of order 5 inspite of strong stability are of no use for practical applications, even if smooth problems are under consideration.