The superconducting elements exclude all magnetic field from their bulk and restrict conduction within a few hundred angstroms of their surface, but there are alloys in which d.c. superconduction occurs in depth. The paper examines the electromagnetic behaviour of both these forms of superconductor, and includes a description of the loss mechanism in hard-alloy superconductors under alternating conditions. It is found that neither form of superconductor could be tolerated in a transformer for practical operation, and an estimate is given of the potential advantage to power transformers of an ideal a.c. superconductor, if one were available.Assuming a hypothetical superconducting film capable of the desired linear current densities while immersed in the appropriate magnetic fields, it is shown that the weight of the core and coils of a large power transformer could be reduced, although not below 39% of the conventional value. Unfortunately, the financial advantage to be expected from the elimination of I2R loss is likely to be more than cancelled by the cost of the refrigeration plant.