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The paper aims to assess the relationship between Azerbaijani and Kazakhstani exchange rates and crude oil prices volatility. The study applies the structural vector autoregressive (SVAR) model. The paper concentrates on Azerbaijan and Kazakhstan, the post-Soviet countries considered as some of the most oil-dependent countries in the Caspian Sea region. The impulse response functions suggest that the rise of crude oil prices is associated with the exchange rates decrease and thus with an Azerbaijani manat and Kazakhstani tenge appreciation against the U.S. dollar. Moreover, the results suggest that an oil price increase leads to the rise of Azerbaijani international reserves. However, the results are insignificant for the Kazakhstani foreign exchange reserves. Additionally, the study reveals a negative and significant relationship between crude oil prices and USD/KZT in both pre-crisis and the COVID-19 crisis periods. We reveal that the correlation has been stronger during the COVID-19 pandemic. However, the relationship is not significant in the case of the Azerbaijani manat. The USD/AZN exchange rate has been stable since 2017, and the first phase of the COVID-19 pandemic has not caused a change in the exchange rate and a weakening of the Azerbaijani currency, despite significant drops in crude oil prices. [ABSTRACT FROM AUTHOR]