As initially formulated, the antisense method for specific inactivation of a nucleic acid target was very straightforward: One utilizes an antisense oligodeoxynucleotide or RNA that hybridizes to a complementary region within a target RNA, thus preventing the RNA from carrying out its normal function [Zamecnik and Stephenson, 1978; Goodchild et al., 1988]. Recently, however, it has become clear that antisense DNA can also operate by a more complex mechanism involving the cleavage of the target RNA by ribonuclease H that is already present in the cell [Minshull and Hunt, 1986; Dash et al., 1987; Walder and Walder, 1988] (see also Minshull and Hunt, this volume). The antisense DNA hybridizes to target RNA and creates a heteroduplex structure that is a substrate for RNase H.