Program slicing has various applications in the fields of software engineering. The Object-Oriented (OO) paradigm introduces the features of abstraction, encapsulation, inheritance, and polymorphism to programs, but is not considered current program slicing techniques. In this paper, we define two types of program slices, state and behavior slices, by taking the dependencies of OO features into consideration. A state slice for an object is a set of messages and control statements that might affect the state of the object, while a behavior slice is a set of attributes and methods defined in related classes that might affect the behavior of the object. These slices may facilitate programmers to debug and understand OO software. The algorithms that developed based on an Object-oriented Dependency Graph to compute these slices can get more precise result by exploring the internal dependencies of complex objects.