<p>Uni-nullnorms and semi-t-operators, as two kinds of significant generalizations of uninorms and t-operators, respectively, have been extensively studied due to their potential applications in many areas such as fuzzy decision making, approximate reasoning and so on. In addition, the distributivity equation related to aggregation functions is of interest in many different theoretical and practical areas. Hence, in this paper, we continue the investigation of this same topic by focusing on uni-nullnorms and semi-t-operators. The results obtained fully characterize the distributivity of uni-nullnorms over semi-t-operators with noncontinuous underlying operators, where uni-nullnorms are disjunctive or conjunctive. Moreover, we show that the distributivity and conditional distributivity of disjunctive or conjunctive uni-nullnorms over semi-t-operators are equivalent under some conditions.</p>