Two types of uncertainties can be generally recognised in structural reliability: natural randomness of basic variables and vagueness of performance requirements. While the randomness of basic variables is handled by common methods of the probability theory, the vagueness of the performance requirements is described by the basic tools of the theory of fuzzy sets. Both, the types of uncertainties are combined in the newly defined fuzzy probabilistic measures of structural reliability, the damage function and the fuzzy probability of failure. The proposed measures can be efficiently applied in a similar way as conventional probabilistic quantities for the verification and optimisation of structural reliability. Adequate data are however needed for further development of the outlined concepts.