The local stability of a technique for iterative solution of continuous nonlinear optimal control problems is considered. The algorithm is based on dynamic integrated system optimisation and parameter estimation, DISOPE, and it is shown that it's local dynamic behaviour can be described in terms of a linear unit-memory repetitive process where the initial conditions change from iteration to iteration. The resulting stability theorem requires the solution of a complex eigenvalue problem. The nature of the solution of this problem is investigated where significant insight is achieved through the use of Maple V symbolic computation. The theoretical results are verified using a MATLAB based graphical user interface specifically developed to analyse these problems.