One of the major requirements for a fusion power plant in the future is tritium self-sufficiency. For this reason the scientific community has dedicated a lot of effort to research activity on reactor tritium breeding blankets. In the framework of the international project DEMO, many concepts of breeding blanket have been taken into account and some of them will be tested in the experimental reactor ITER by means of appropriate test blanket modules (TBMs). All the breeding blanket concepts rely on the adoption of binary systems composed of a material acting as neutronic multiplier and another as a breeder. This paper addresses a neutronic feature of these kinds of systems. In particular, attention has been focused on the assessment of the importance of neutrons coming from multiplication reactions for the production of tritium. A theoretical framework has been set up and a procedure to evaluate the performance of the multiplier-breeder systems, under the aforementioned point of view, has been developed. Moreover, the model set up has been applied to helium cooled lithium lead and helium cooled pebble bad TBMs under irradiation in ITER and the results have been critically discussed.