The connectionist network corresponding to the nonlinear integration dynamical system associated with Kintsch's construction-integration (CI) model is analysed with linear algebra tools. This addresses some theoretical questions raised and left unanswered by Rodenhausen (1992, Psychological Review 99, 547-549). A mathematical characterization for equilibrium points, which allows an a priori enumeration of all possible asymptotic states for the integration dynamical system, given a connectivity matrix, is given. The dynamics of convergence of the integration dynamical system is characterized in some detail as well. This provides a tool for understanding CI simulations and helps in particular to let us know to what extent the outcome will depend on the initial conditions. The criteria also provide a new mathematical analysis which allows for the explicit calculation of asymptotic states of the integration process without requiring computer simulation experiments. The new mathematical analysis should facilitate comparisons of the model's predictions with behavioural data. Copyright 2001 Academic Press.