  We discuss two non-standard models of nonadaptive combinatorial search which
develop the conventional disjunct search model for a small number of defective
elements contained in a finite ground set or a population. The first model is
called a search of defective supersets. The second model is called a search of
defective subsets in the presence of inhibitors. For these models, we study the
constructive search methods based on the known constructions for the disjunct
model.
