  We consider a semistable degeneration of K3 surfaces, equipped with an
effective divisor that defines a polarisation of degree two on a general fibre.
We show that the map to the relative log canonical model of the degeneration
maps every fibre to either a sextic hypersurface in P(1,1,1,3) or a complete
intersection of degree (2,6) in P(1,1,1,2,3). Furthermore, we find an explicit
description of the hypersurfaces and complete intersections that can arise,
thereby giving a full classification of the possible singular fibres.
