A new topological approach is proposed for the analysis of change in group structure over time. Special force fields are defined operationally to explain changes in the structure, which are estimated by a method called DYNASCAL, given a set of longitudinal dissimilarity judgements such as longitudinal sociograms. These fields are presumably generated by interactions among individuals. For theoretical simplicity, these fields are supposed to be two-dimensional vector fields, which are described by a system of general nonlinear differential equations. Qualitative theories of the dynamical system such as those of singularities, bifurcations, and structural stability of the vector field are shown to be useful for describibg qualitative aspects of the force fields. Some difficulties in application of our method to empirical data are indicated and ways of overcoming them are discussed