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This study estimates the demand for international reserves function in Nigeria using vector auto-regressions, and annual time-series data for 1980-2017. The result obtained indicates that there is a stable, long-run relationship between international reserves, exports, openness, interest rate and export earnings volatility. Variance decomposition analysis shows the main sources of economic growth variations in Nigeria are attributable to "own shocks" and only slightly to other variables, namely, exports and openness. Thus, the study recommends that the government should adopt trade and exchange rate policies to promote exports in order to increase international reserve holdings and accelerate economic growth in Nigeria.