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The propagation of single event transients (SET) is measured and modeled in SOI and bulk inverter chains. The propagation-induced pulse broadening (PIPB) effect is shown to determine the SET pulse width measured at the output of long chains of inverters after irradiation. Initially, narrow transients, less than 200 ps at the struck inverter, are progressively broadened into the nanosecond range. PIPB is induced by dynamic floating body effects (also called history effects) in SOI and bulk transistors, which depend on the bias state of the transistors before irradiation. Implications for SET hardness assurance, circuit modelling and hardening are discussed. Floating body and PIPB effects are usually not taken into account in circuit models, which can lead to large underestimation of SET sensitivity when using simulation techniques like fault injection in complex circuits.