The coincidence of flood flows in a mainstream and its tributaries may lead to catastrophic floods. In this paper, we investigated the flood coincidence risk under nonstationary conditions arising from climate changes. The coincidence probabilities considering flood occurrence dates and flood magnitudes were calculated using nonstationary multivariate models and compared with those from stationary models. In addition, the "most likely" design based on copula theory was used to provide the most likely flood coincidence scenarios. The Huai River and Hong River were selected as case studies. The results show that the highest probabilities of flood coincidence occur in mid-July. The marginal distributions for the flood magnitudes of the two rivers are nonstationary, and time-varying copulas provide a better fit than stationary copulas for the dependence structure of the flood magnitudes. Considering the annual coincidence probabilities for given flood magnitudes and the "most likely" design, the stationary model may underestimate the risk of flood coincidence in wet years or overestimate this risk in dry years. Therefore, it is necessary to use nonstationary models in climate change scenarios.