Dose-response curves for the first interaction of a chemical with a biochemical target molecule are usually monotonic; i.e., they increase or decrease over the entire dose range. However, for reactions of a complex biological system to a toxicant, nonmonotonic (biphasic) dose-effect relationships can be observed, showing a decrease at low dose followed by an increase at high dose, or vice versa. We present four examples to demonstrate that nonmonotonic dose-response relationships can result from superimposition of monotonic dose responses of component biological reactions. Examples include (i) a membrane-receptor model with receptor subtypes of different ligand affinity and opposing downstream effects (adenosine receptors A1 vs. A2), (ii) androgen receptor-mediated gene expression driven by homodimers, but not mixed-ligand dimers, (iii) repair of background DNA damage by enzymatic activity induced by adducts formed by a xenobiotic, (iv) rate of mutation as a consequence of DNA damage times rate of cell division, the latter being modulated by cell-cycle delay at low-level DNA damage, and cell-cycle acceleration due to regenerative hyperplasia at cytotoxic dose levels. Quantitative analyses based on biological models are shown, and factors that affect the degree of nonmonotonicity are identified. It is noted that threshold-type dose-response curves could in fact be nonmonotonic. Our analysis should promote a scientific discussion of biphasic dose responses and the concept termed "hormesis," and of default procedures for low-dose extrapolation in toxicological risk assessment.