Expression levels of individual copies of an inducible gene have been presumed to be identical to the averaged level of many copies and to change in a smooth and predictable way according to the concentration of an inducing molecule. However, our recent experiments using a steroid-inducible system showed that the expression levels of individual copies are very heterogeneous and do not necessarily coincide with the averaged expression level of many copies (Ko et al., 1990, EMBO J. 9, 2835-2842). To explain this result, I present a stochastic model for gene induction here and its analysis using computer simulation. Stochasticity in the model is derived from the randomness corresponding to the random timing of molecular collisions and dissociations between transcription factors and a gene copy, since at any instant each copy is thought to be either "switched on" by having a transcription complex bound to it, or "switched off" by not having a transcription complex bound. This model can produce two types of gene induction that depend on the stability of the transcription complex on the regulatory region of the gene. An unstable transcription complex causes a homogeneous level of gene induction among individual copies, while a stable transcription complex causes a heterogeneous level. Since the recent consensus formed by in vitro transcription experiments is that the transcription complex is generally very stable, the latter case (the non-deterministic one) is highly possible. Since typical eukaryotic cells have just two copies for any gene in a single cell, this possibility of heterogeneous gene induction indicates that the phenotypes of individual cells cannot be precisely determined by just environmental signals, such as inducers. This may prompt us to reconsider many problems related to gene induction, including morphogenesis.