Punctuality is a sensitive issue in large airports and hubs for passenger experience and for controlling operational costs. This paper presents a real and challenging problem of predicting and explaining flight off-block delays. We study the case of the international airport Paris Charles de Gaulle (Paris-CDG) starting from the specificities of this problem at Paris-CDG until the proposal of modelings then solutions and the analysis of the results on real data covering an entire year of activity. The proof of concept provided in this paper allows us to believe that the proposed approach could help improving the management of delays and reduce the impact of the resulting consequences.