The influence of membrane-perturbing drugs such as anaesthetics on the lipid membrane properties is analyzed theoretically on the basis of a general microscopic interaction model of the gel-to-fluid chain melting transition of one-component phospholipid membranes and phospholipid membranes with a low content of cholesterol. Monte Carlo computer simulation of the model shows that the gel-to-fluid transition of the lipid membrane, manifested in the formation of dynamically coexisting domains of gel and fluid lipids, is strongly influenced by the presence of anaesthetics. Macroscopically the effect of anaesthetics on the membrane properties is seen in a depression of the transition temperature and a smearing of thermodynamic response functions like the specific heat. Microscopically the calculations reveal that anaesthetics have a high affinity to the fluctuating domain interfaces that are dominated by kink-like lipid-chain conformations. This leads to formation of more interfaces and to a locally high concentration of anaesthetics in the interfacial regions, which is much larger than the global concentration in the membrane. Important membrane components like cholesterol, which also has been shown to be interfacially active, are found to decrease the absorption of anaesthetics and to squeeze out anaesthetics from the interfaces. The results of the general model study of anaesthetics-membrane interactions are discussed in relation to both general anaesthetics, like halothane, and local anaesthetics like cocaine-derivatives.