The total generalised colourings considered in this paper are colourings of the vertices and
of the edges of graphs satisfying the following conditions:
• each set of vertices of the graph which receive the same colour induces an
• each set of edges of the graph which receive the same colour induces an n-degenerate
• incident elements receive different colours.
Bounds for the least number of colours with which this can be done for all k-degenerate
graphs are obtained.