This paper presents an empirical analysis of the demand for maize, milk powder, butter, and rice imports in Cyprus, using annual time series data covering the period 1975–1994. None of these products is produced in Cyprus and all the necessary quantities are imported to meet domestic demand. The primary objective of the paper is to derive long-run price and income elasticities of import demand that can be used to analyse the impact of various policies such as the adoption of the Common Agricultural Policy (CAP) when, and if, the Republic of Cyprus joins the European Union (EU). In so doing the paper takes on board some recent developments in time series econometrics. The cointegration test used (the ‘bounds’ test) is a recent test and is based on the estimation of an unrestricted error-correction model (UECM). Parsimonious models were derived using Hendry's ‘general to specific’ approach. The estimated elasticities were subsequently used to quantify some of the implications for Cyprus had the CAP been operational in 1994.