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Models with a wide technological representation of energy systems can hardly adopt hourly resolutions to study the energy transition towards low-carbon technologies due to extended problem size. This compromises the model's ability to address the challenges of variable renewable energy sources and the cost-effectiveness of cross-sectoral flexibility options. This methodology presents a linear program model formulation that simultaneously adopts different temporal representations for different parts of the problem to overcome this issue. For instance, all electricity activities and their infrastructure representation require hourly constraints to better replicate system feasibility. The operation of gaseous networks is settled out with daily constraints. The balancing of the other activities of the system is represented with yearly constraints. Furthermore, the methodology adopts an hourly formulation to represent in detail 6 cross-sectoral flexibility archetypes: heat and power cogeneration, demand shedding, demand response, storage, smart charging and electric vehicles. The model can successfully solve the transition problem from 2020 to 2050 in 5-year intervals with more than 700 technologies and 140 activities (including the electricity dispatch of the Netherlands and 20 European nodes) in less than 6 hours with a normal computer. • Different temporal scales for the representation of different activities in the energy system. • A high-resolution hourly description for the formulation of cross-sectoral flexibility in integrated energy models., Competing Interests: The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper., (© 2022 The Authors.)