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The concept of (k, l)-kernels of digraphs was introduced in . Next, H. Galeana-Sanchez [?] proved a sufficient condition for a digraph to have a (k, l)-kernel. The result generalizes the well-known theorem of P. Duchet and it is formulated in terms of symmetric pairs of arcs. Our aim is to give necessary and sufficient conditions for digraphs without symmetric pairs of arcs to have a (k, l)-kernel. We restrict our attention to special superdigraphs of digraphs P m and C m .doi:10.7151/dmgt.1135 fatcat:hg25hii4uje37gyhzwsoiwutjy