The paper develops expressions for the self- and mutual-inductance coefficients of machine windings for the general case of nonsinusoidal winding distributions and nonuniform air gap. These expressions involve the harmonics of the winding distribution and the air-gap permeability. For some sample cases, numerical values are given and the departures from the ideal sinusoidal case assessed.The coefficients evaluated in the paper are those which form the starting point of the generalised mathematical theory of machines. The results are of significance in showing how, and to what extent, departures from the ideal machine modify the coefficients and introduce new terms not amenable to the usual mathematical treatment.