An extensive computer-simulation study is performed on a simple but general molecular model recently proposed (Jørgensen et al. (1991) Biochim. Biophys. Acta 1062, 227-238) to describe foreign molecules interacting with lipid bilayers. The model is a multi-state lattice model of the main bilayer transition in which the foreign molecules are assumed to intercalate at interstitial lattice positions. Specific as well as non-specific interactions between the foreign molecules and the lipid acyl chains are considered. Particular attention is paid to the fluctuating properties of the membrane and how the presence of the foreign molecules modulates these fluctuations in the transition region. By means of computer-simulation techniques, a detailed account is given of the macroscopic as well as microscopic consequences of the fluctuations. The macroscopic consequences of the fluctuations are seen in the thermal anomalies of the specific heat and the passive trans-membrane permeability. Microscopically, the fluctuations manifest themselves in lipid-domain formation in the transition region which implies an effective dynamic membrane heterogeneity. Within the model it is found that certain anaesthetics and insecticides which are characterised by specific interactions with the lipids have a strong effect on the heterogeneity of the membrane inducing regions of locally very high concentration of the foreign molecules. This leads to a broadening of the specific heat peak and a maximum in the membrane/water partition coefficient. These results are in accordance with available experimental data for volatile general anaesthetics like halothane, local anaesthetics like cocain derivatives, and insecticides like lindane.