Existent software does not seem to be able to cope with situations where two conductors slide on each other, with current going through the interface. Modelling a homopolar dynamo, for instance, would require this capability. We extend standard eddy current theory to cover this case, and describe the basic algorithm. The approach is Lagrangian in spirit. Degrees of freedom (DoF), edge-based, are time-integrals of edge-EMFs as expressed in the local (comoving) reference frame, and are related to the vector potential. When two surfaces slide on each other, DoFs on them are linked by a matching relation (that can be formed by using 2D edge elements on the sliding surface), which expresses the tangential continuity of the vector potential at each instant. (The comoving electric field does not exhibit such continuity, and cannot be used as primary variable. This is explained by the difference between (time-) partial derivative and "convective", or total, derivative.) No v×b terms appear in the theory, and minimal adaptation is required to turn a standard code into one able to treat sliding contacts, the only additional feature being the matching relation. (2 pages)