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 in 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 developed to compute these slices that are based on an OO dependency graph can obtain more precise results by exploring the internal dependencies of complex objects.