© 2017 Elsevier Inc. Aggregation operators play an important role in many theoretical and practical aspects of applied mathematics. Recently, the focus is on operators with an annihilator, therefore the topic of this paper is distributivity, both conditional and regular, for certain classes of aggregation operators with this property. The characterization of all pairs (F, G) of aggregation operators that are satisfying distributivity law, on both whole and restricted domain, where F is a T-uninorm in Umax, and G is a t-conorm or a uninorm from Umin or Umax is given.