The feasibility of solving 2-dimensional saturable eddy-current problems using an alternating-direction-implicit method to solve the finite-difference equations has been investigated. A simple single-dimensional problem has been tackled in a 2-dimensional manner, and results compared with existing single-dimensional solutions. Saturation is represented by the Fröhlich equationB=H(a+bH)−1. Only one recalculation of reluctivity per time step has been used. This gives substantial savings in computing time and cost, although the method is accurate only for mild nonlinearity. Stronger nonlinearity, representative of heavily saturated parts of the magnetic circuit of electrical machines, requires reluctivity iteration at each time step. The improvement of convergence, by suitable choice of underrelaxation factor, is demonstrated, and also the failure of two possible accelerative procedures using line-integral and surface-integral correction.