In recent months, the crude oil market has shown an abnormal behavior as compared with the previous 20 years. The most relevant feature of it being the high-level prices, well beyond the most pessimistic forecasting of a couple of years ago. The aim of this paper is to show that the crude oil price dynamics in the period from mid-2003 to late-2004 can be described by a piecewise linear increasing trend plus an oscillatory behavior with power-law periodicity. In about mid-December 2003, a transition in the period of the price oscillations was detected. Before and after such a date, the oscillation period decreased and increased with time, respectively. Additionally, after July, 2004, the slope of the trend has suffered a 200% increment, which may indicate that the market instability is becoming stronger.