We study the relationship between daily oil prices and nominal exchange rates between 1995 and 2019 in Colombia through a Time-Varying Vector Auto-Regressions with residual Stochastic Volatility, TV-VAR-SV, model. For this task we also employ co-integration, Univariate Auto-Regressions with residual Stochastic Volatility, UAR-SVTV, and De-trended Cross Correlation, DCC analyses. We found that a stable lon-grun relationship between the two processes is lacking. We also found significant time variation in residual volatility and co-volatility. More specifically, we found that both periods of time, the international financial crisis and the oil price drop of 2015, behave conspicuously different from other “more normal” times. These results are consistent with a shift in the features of the DCC at the start of the crisis. Before the crises the DCCs are positive but weak for different windows sizes, turning negative and significant after it. The latter DCCs and their significance increase with the window size. These results are concurrent, also, with two clearly differentiated periods of time; one when oil production was not financially feasible, and thus production, exports and oil related currency inflows were small, and the other when oil production became feasible because of the price increase, which led to a boom in exploration, production, exports and oil related currency inflows.