The comportment of the price of WTI oil is complex, and it is characterised by rises, falls, abrupt changes and local trends. As a result, it is difficult to identify the impact of exogenous events on the market in the comportment of prices, and as these impacts cannot be easily isolated, the dynamics of the series become obscure and difficult to predict. In preliminary inspection of the natural logarithm series of the average monthly price of WTI between 1986:1 and 2008:8 gives rise to suspicion of the presence of local linear trends which ended in evident changes in dynamics. In order to validate this appreciation, an algorithm was developed for research based on a recursive partitioning to detect points of occurrence of structural changes in the trend. The algorithm was used to analyse the dynamics of the series studied. The principal results: returns of prices followed a process AR (1)-GARCH (2, 2), and there are three statistically significant structural changes, which are explained by its specific historic events. These changes of level show the existence of local linear trends in the prices logarithm.