The nonlinearities of US oil markets(WTI crude oil, No 2 heating oil, and regular gasoline) has been investigated during the period after 2000 in terms of exploratory analysis, estimation, and in-sample prediction accuracy. Exploratory analysis showed the following findings. First, the mean returns of product oil markets were higher than those of WTI crude oil markets. Second, WTI crude oil markets has been turned into contango since 2004, and product oil markets showed earlier transition into contango than WTI crude oil markets. These phenomena can be related to the fact that the price trend in US oil markets had remained relatively unchanged without any big upward movements by then. Finally, in terms of arbitragers' investment behaviors by market conditions, WTI crude oil markets were targeted more frequently by arbitragers than product oil market and contango was favored by arbitragers than backwardation. These phenomena can be caused by the fact that buying spots and selling futures contracts under the contango is more feasible investment strategy than the opposite in reality. WTI crude oil and No 2 heating oil markets had an even composition of linear models and nonlinear ones as better estimation ones while regular gasoline markets tended to be better estimated with linear models. Prediction had a different story from estimation. Linear models had relatively better prediction accuracy across the sub-samples although nonlinear models had the same prediction accuracy as linear ones in the sub-samples except those of "Group 1".