Innovative reactor concepts make use of passive safety features to a large extent in combination with active safety or operational systems. Following the IAEA definitions a passive component does not need external input (especially energy) to operate. This is why it is expected that passive systems combine among others the advantages of simplicity, reduction of the need for human interaction, reduction or avoidance of external electrical power or signals. Besides the open feed-back on economic competitiveness special aspects like lack of data on some phenomena, missing operating experience over the wide range of conditions and the smaller driving forces as - in most cases - compared to active safety systems must be taken into account. Both for active and passive systems, the effective reliability versus the achievement of safety functions is considered as an essential criteria for judging the real potential of the systems. Generally speaking, the reliability assessment of passive safety functions defined as the probability to fail the requested mission to achieve a generic safety function, depends, more than for active systems, on environment, physical, nuclear or chemical phenomena. This remark is entirely applicable to the passive B systems (i.e. implementing moving workingfluids, cf. IAEA). Their mission is defined through a nominal requested time dependent evolution, for a set of selected and representative parameters and an allowable range is allocated around the nominal evolution. It is stated that the mission fails when the plant parameters are outside the allowable range.As a first approach, it is considered that the reliability assessment of passive safety functions can be estimated evaluating the probability for having the mission failure. This assessment is achieved comparing the distribution of the expected parameters values to the allowable range.This implies the identification and quantification of the uncertainties in the prediction of physical phenomena performances or interdependencies. In parallel, an adequate effort must be devoted to the improvement of thermalhydraulic computer codes that model the passive safety system behaviour to integrate those uncertainties. Finally, the transfer of the structural methodology assessment methodology (i.e. for passive A systems) must be checked to verify its applicability for the thermalhydraulic passive systems, tooThe paper is focused particularly on passive B safety functions and related systems and illustrates a possible methodology for their reliability assessment.The example explained in the report can be used as a preliminary basis to motivate and to organise the content of a work that could be conducted within the framework of the European Commission sponsored activities on Reliability Methods for Passive Safety Functions.