Manipulating force and grasping force for skillful manipulation of objects by multifingered robot hands are discussed in this paper. A new representation of the internal force among the fingers is given. Based on this representation, the grasping force is defined as an internal force which satisfies the static friction constraint. The mode of grasping is also introduced. The manipulating force is then defined as a fingertip force which satisfies the following three conditions: 1) It produces the specified resultant force. 2) It is not in the inverse direction of the grasping force. 3) It does not contain any grasping force component. An algorithm for decomposing a given fingertip force into manipulating and grasping forces is presented.