Siberian Federal University

Multifunctions on a two-element set are considered in this paper. Functions from finite set to set of all subsets of this set are called multifunctions. Partial functions, hyperfunctions, ultrafunctions, par- tial hyperfunctions and partial ultrafunctions are arised depending on the type of multifunctions and superposition. In this work the problem of description of clones (sets of function closed with respect to the operation of superposition and containing all the projections) of partial ultrafunctions is considered. We got a description of one maximal clone of partial ultrafunctions on two-element set by the predicate approach