The functional stability and lifetimes of synthetic molecular circuits in biological environments are important for long-term, stable sensors or controllers of cell or tissue behavior. DNA-based molecular circuits, in particular DNA strand-displacement circuits, provide simple and effective biocompatible control mechanisms and sensors, but are vulnerable to digestion by nucleases present in living tissues and serum-supplemented cell culture. The stability of double-stranded and single-stranded DNA circuit components in serum-supplemented cell medium and the corresponding effect of nuclease-mediated degradation on circuit performance were characterized to determine the major routes of degradation and DNA strand-displacement circuit failure. Simple circuit design choices, such as the use of 5' toeholds within the DNA complexes used as reactants in the strand-displacement reactions and the termination of single-stranded components with DNA hairpin domains at the 3' termini, significantly increase the functional lifetime of the circuit components in the presence of nucleases. Simulations of multireaction circuits, guided by the experimentally measured operation of single-reaction circuits, enable predictive realization of multilayer and competitive-reaction circuit behavior. Together, these results provide a basic route to increased DNA circuit stability in cell culture environments.