Abstract. Space and time play a crucial role in multi-hazard impact assessment. When two or more natural hazards occur at the same location simultaneously or within a short time frame, the physical integrity of assets and infrastructures can be compromised and the resulting damage can be greater than the one generated by individual hazards occurring in isolation. The current literature highlights the lack of quantitative standardised frameworks for multi-hazard impact assessment. This research presents a generalised mathematical framework for quantitatively assessing multi-hazard physical damage on exposed assets, such as buildings or critical infrastructures, over time. The proposed framework covers both concurrent and consecutive hazards, by modelling: (i) the increased damage resulting from the combined impact of two or more concurrent hazards that overlap in space and time, and (ii) the effects of cumulative damage on asset vulnerability and the recovery dynamics in case of consecutive hazards that overlap in space. The framework is applied to a real-world case study in Puerto Rico, including the concurrent wind and flood impacts generated by the passage of Hurricane Maria, as well as the consecutive impacts caused by the subsequent seismic sequence of 2019–2020. Based on simulations performed on a building portfolio, we found that neglecting residual damages caused by the hurricane when assessing the impacts of the subsequent earthquake would lead to a significant underestimation of the overall damage experienced by the assets. By providing a generalised formalisation to perform quantitative multi-hazard impact assessment, able to account for amplification phenomena and recovery dynamics, the framework can offer scientists and decision-makers a comprehensive and deeper understanding of the impacts caused by compound and consecutive events.