An arc-coloured digraph is alternating if whenever and are arcs in they are of different colours. In an arc coloured digraph , a subset of vertices of is a kernel by alternating paths (or alternating kernel) if it is absorbent and independent by directed alternating paths. In this paper we prove sufficient conditions for the existence of alternating kernels in arc-coloured tournaments, quasi-transitive digraphs, and -partite digraphs.