The thermal evolution of organic matter (OM) is composed of a series of reactions that are paralell and successive with each other. Different reactions have different activation energy, different rates of product concentration variation, and different volume expansion effects,and therefore have different responses to overpressure, which determines the differential retardation of different OM maturation reactions and maturity parameters. Based upon comprehensive studies on the OM maturation in different pressure systems in the Yinggehai, Qiongdongnan and Bohai Bay basins, 4 hierarchies of overpressure retardation have been recognized. (1) OM maturation in all aspects has been retarded by overpressure. (2) The thermal evolution of hydrocarbons and thermal degradation of hydrogen-rich kerogens has been retarded, but the thermal evolution of hydrogen-poor kerogen components has not been affected by overpressure.As a result, vitrinite reflectance has not been retarded. (3) The thermal cracking of hydrocarbons has been retarded, yet overpressure has had little or no effect on thermal degradation of kerogens. (4) Overpressure has no detectable effect on all aspects of OM maturation. The hierarchy that overpressure has retarded all aspects of OM maturation is the combined result of "early"overpressure (overpressure began to develop when the source rock was still immature) and the protracted maintenances of closed fluid system. Any case that overpressure had developed too late, or overpressure was too small to reach the threshold values, or overpressured fluid had been frequently released, could give rise to the occurrence of state 4 that overpressure had no detectable effect on all aspects of OM maturation. It seems that in many basins, overpressure retardation of hierarchies 2 and 3 developed where the most commonly used maturity parameter,vitrinite reflectance, had not been affected. In theses cases, multiple parameters must be used to distinguish overpressure retardation.