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The paper develops a particularly direct form of model for reactive-power compensators that are based on saturated reactors. It is one in which each winding section of each limb of the main- and auxiliary-core structures is represented individually together with its core nonlinear magnetic-circuit characteristics. Depending on the precise internal configuration, there may be 30-50 individual winding sections. The complete model is of a transient form, and it is shown in the paper how it may be combined with a powerful z-plane electromagnetic transient formulation for network systems in which a saturated reactor compensator is one element. As it is in general form, the compensator model makes provision for representing the particular main- and auxiliary-core systems of any given design such as those of the twin tripler and triple tripler compensators. Particular cases are selected by data items. Both the model itself and its programming implementation are completely general. The validity of the model developed is examined on the basis of comparisons between computer-simulation solutions and sitetest recordings of the main compensator variables following the energisation of a compensatorterminated line section. In one particular aspect of the correlation, computer simulation reproduces closely the subharmonic oscillations arising from the slope-correcting capacitors and the complex saturating magnetic system of a twin tripler compensator.