An edge colouring of a graph is said to be an r-local colouring if the
edges incident to any vertex are coloured with at most r colours.
Generalising a result of Bessy and Thomass\'e, we prove that the vertex set of
any 2-locally coloured complete graph may be partitioned into two disjoint
monochromatic cycles of different colours. Moreover, for any natural number
r, we show that the vertex set of any r-locally coloured complete graph may
be partitioned into O(r2logr) disjoint monochromatic cycles. This
generalises a result of Erd\H{o}s, Gy\'arf\'as and Pyber.Comment: 10 page