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SUMMARYThis paper presents a theoretical analysis of the effect of duration on the damage of structures subjected to earthquakes. The earthquake excitation is modelled by a non-stationary random process whose response spectrum is probabilistically consistent with a design response spectrum specified independently of the duration. Damage is assumed to accumulate with the cyclic application of large strains in the structural members. Two types of structure are examined: one representative of a steel structure and the other reprsentative of a reinforced concrete structure. The level of expected damage is found to be a strong function of both the ductility of the response and the duration of the excitation. Results are presented for systems with linear stiffness and a particular form of softening behaviour.