Background. Fluctuations in alcohol consumption in Greenland have been extreme since alcohol became available to the Greenland Inuit in the 1950s, increasing from low levels in the 1950s to very high levels in the 1980s about twice as high as alcohol consumption in Denmark. Since then, consumption has declined, and current consumption is slightly below alcohol consumption in Denmark, while alcohol prices are far above Danish prices. Objective. Description of historical trends and possible causal connections of alcohol prices, alcohol consumption and alcohol-related mortality in Greenland 1951-2010 as a background for the evaluation of the impact of various types of policy. Design. Time series for Greenland 1951-2010 for alcohol prices, consumption and mortality are compiled, and variation and correlations are discussed in relation to various policies aimed at limiting alcohol consumption. Corresponding time series for Denmark 1906-2010 are presented for comparison. Results. The trends in alcohol prices and consumption followed each other rather closely until the 1990s in Greenland and the 1980s in Denmark. At this time, consumption stabilised while prices decreased further, but the effect of prices upon consumption is strong, also in recent years. A trend in Greenlandic mortality similar to consumption is discernible, but not significant. Among alcohol-related deaths cirrhosis of the liver is less prevalent whilst accidents are more prevalent than in Denmark. Conclusions. The effect of alcohol excise taxes and rationing upon consumption is evident. The stabilisation and subsequent decline in consumption since the mid-1990s, while alcohol prices decreased persistently, does not preclude continued effects of prices. On the contrary, price effects have been neutralised by other stronger causes. Whether these are government anti-alcohol campaigns or a cultural change is not clear.