A novel and general approach is described for generating versions of RNA-cleaving ribozymes (RNA enzymes) and DNAzymes (DNA enzymes), whose catalytic activity can be controlled by the binding of activator molecules. Variants of the RNA-cleaving 10-23 DNAzyme and 8-17 DNAzyme were created, whose catalysis was activated by up to approximately 35-fold by the binding of the effector adenosine. The design of such variants was possible even though the tertiary folding of the two DNAzymes is not known. Variants of the hammerhead ribozyme were constructed, to respond to the effectors ATP and flavin mononucleotide. Whereas in conventional allosteric ribozymes, effector-binding modulates the chemical step of catalysis, here, effectors exercise their effect upon the substrate-binding step, by stabilizing the enzyme-substrate complex. Because such an approach for controlling the activity of DNAzymes/ribozymes requires no prior knowledge of the enzyme's secondary or tertiary folding, this regulatory strategy should be generally applicable to any RNA-cleaving ribozyme or DNAzyme, natural or in vitro selected, provided substrate-recognition is achieved by Watson-Crick base-pairing.