Agents being a kind of restricted intelligent objects, it is a natural way to research the inheritance feature of software agents and integrate inheritance mechanisms into AOP. Based on BDI model of agents, this paper addresses the semantics of static inheritance and dynamic inheritance of agents. For static inheritance, the semantics are discussed from two angles: single inheritance and multiple inheritance. For dynamic inheritance, we identify and formally classify the behavior of dynamic cloning of agent instances into four types: function split, logic split, preference split and retrogress split. The mechanism of each type of cloning is presented and examples are provided based on electrical commerce systems.