Introduction D the last few years, a considerable amount of effort has been put into the development of new methods of analysis for nonlinear structural systems. Taking advantage of the capabilities of modern electronic computers, these methods have been widely applied to problems of large deformations and stability, elasto-plasticity, creep, etc. Often, the numerical solution of these nonlinear problems is based on some iterative process or it involves the combination of an incremental and an iterative procedure. An ever-recurrent problem associated with iterative techniques is the decision as to whether the current iterate is sufficiently close to the root without knowing the true solution itself. In the following, a discussion of the convergence problem will be given and some practical convergence criteria will be presented. For simplicity, a pure displacement formulation of the structural problem will be assumed.