Various theoretical expressions are presented for determining risk in water resources systems design based on floods modelled by dependent processes. The effect of dependence on the simple risks involved in any engineering design is investigated on the basis of the lag-one Markov process. Asymptotically dependent process formulations reduce to independent case solutions that are already available in the literature. It is shown that a design risk value can be determined if the expected project life, serial correlation coefficient and simple risk are known. Necessary procedures and tables are presented for risk calculations when the variables concerned are serially correlated.