The use of variable scalar step-lengths can significantly improve the convergence characteristics of iterative solution procedures. These step-lengths can be calculated in two-different ways; in a corector sense using 'line-searches' or in a predictor sense using some acceleration scheme. Both versions are considered in the present report and the resulting variable step-lengths are applied to non-linear finite element analyses implementing the Newton-Raphson and modified Newton-Raphson interative solution procedures. The variable step-length algorithms are incorporated in incremental formulations using both load control and the more versatile 'arc-length' method