Four time-series models are introduced for analysing the demand for addictive substances. The models are applied to estimate the demand for tobacco products in Finland. Separate models were found appropriate for different products. The price of cigarettes is the most important single determinant of the demand for tobacco products. The demand for cigarettes is twice as sensitive to falling prices (elasticity - 0.94) than to rising prices (elasticity - 0.49). The demand for cigarettes is also responsive to changes in real income. The most important factor influencing the demand for pipe tobacco is the price of cigarettes. The demand for cigars is adequately explained by changes in its price. The 1977 Tobacco Act and the anti-smoking publicity preceding it appear to have reduced the cigarette demand permanently by 7%. The results imply that taxation would seem a powerful instrument for achieving the objectives of restricting consumption of tobacco products and raising government revenue. Yet, taxation together with extensive anti-smoking publicity would have a more advantageous effect than either of them used in isolation.