This thesis tackles the problem of automatically synthesizing motions of close-character interactions which appear in animations of wrestling and dancing. Designing such motions is a daunting task even for experienced animators as the close contacts between the characters can easily result in collisions or penetrations of the body segments. The main problem lies in the conventional representation of the character states that is based on the joint angles or the joint positions. As the relationships between the body segments are not encoded in such a representation, the path-planning for valid motions to switch from one posture to another requires intense random sampling and collision detection in the state-space. In order to tackle this problem, we consider to represent the status of the characters using the spatial relationship of the characters. Describing the scene using the spatial relationships can ease users and animators to analyze the scene and synthesize close interactions of characters. We first propose a method to encode the relationship of the body segments by using the Gauss Linking Integral (GLI), which is a value that specifies how much the body segments are winded around each other. We present how it can be applied for content-based retrieval of motion data of close interactions, and also for synthesis of close character interactions. Next, we propose a representation called Interaction Mesh, which is a volumetric mesh composed of points located at the joint position of the characters and vertices of the environment. This raw representation is more general compared to the tangle-based representation as it can describe interactions that do not involve any tangling nor contacts. We describe how it can be applied for motion editing and retargeting of close character interaction while avoiding penetration and pass-throughs of the body segments. The application of our research is not limited to computer animation but also to robotics, where making robots conduct complex tasks such as tangling, wrapping, holding and knotting are essential to let them assist humans for the daily life.