It is shown that the classical induction-machine model does not correctly take into account the actual saturation effects of the magnetising field in situations different from sinusoidal supply/steady state conditions. An improved set of stationary equations is derived, making more accurate allowances for the magnetising-field saturation. Owing to saturation, both this modified nonlinear 2-axis model and the modified linearised model (small signal model) derived from it are not symmetrical with respect to the two axes. Indeed, for the calculation of transients or dynamics of a saturated machine, one has to consider two different magnetising inductances for the two axes. This point of view is also confirmed by experiments. The paper is in two parts. Part 1 contains the derivation of the corrected machine model and a concise report on an experimental confirmation of it. In Part 2, some practical applications of the proposed machine model concerning dynamic behaviour are discussed. Such applications constitute further proofs in support of the correctness of the proposed theory.