The convergence properties of a general iterative (off-line) pseudo-linear regression (PLR) algorithm are examined. It is found that the basic form of the algorithm converges under quite restrictive conditions. A simple modification of the algorithm is then proposed which relaxes the convergence conditions considerably. The refined PLR algorithm converges under precisely the same conditions as the well-known recursive (on-line) PLR procedure. The problem of monitoring the algorithm to guarantee the stability of estimated models is also discussed. A modified PLR algorithm which does not require monitoring is proposed, and its convergence properties analysed. Finally, some numerical examples illustrating the main theoretical results are included.