In conventional polyphase alternating-current machines, the number of parallel circuits per phase is always an integral submultiple of the pole number. This requirement can impose restrictions in relation both to the optimisation of design, and to the practical aspects of the manufacture of medium and large low-voltage machines. A general method is described in this paper, by which several alternative intermediate numbers of parallel circuits per phase and numbers of parallel circuits greater than the pole-number can be derived, for a wide range of combinations of armature slot number and pole number. The design and performance of a 4-pole machine with six parallel circuits per phase, and of a 6-pole machine with four parallel circuits per phase, are considered in detail, by way of example. The new windings are of the double-layer type. It is shown that, on the basis of identical coil pitches, the new type of winding is not inferior in rating or load performance to a standard winding; and that, in addition to the advantage of a free choice of the number of parallel paths, there is the further advantage of improved accelerating characteristics.