An　oriented　path　P　is　called　anti-directed　if　every　two　consecutive　arcs　of　P　have　opposite　orientations.　An　oriented　graph　is　called　k-anti-traceable　if　every　subdigraph　induced　by　k　vertices　has　a　hamiltonian　anti-directed　path.　We　introduce　and　study　a　conjecture,　which　claims　that　for　every　integer　k　＞=　2　there　is　a　least　integer　f　(　k　)　such　that　each　k-anti-traceable　oriented　graph　on　f　(　k　)　vertices　has　a　hamiltonian　anti-directed　path.　We　determine　f　(2),　f　(3),　f　(　4　)　and　show　that　every　k-anti-traceable　oriented　graph　on　sufficiently　large　number　n　of　vertices　admits　an　anti-directed　path　that　contains　all　but　o　(　n　)　vertices.　(c)　2024　The　Authors.　Published　by　Elsevier　B.V.　This　is　an　open　access　article　under　the　CC　BY　license　(http://creativecommons　.org　/licenses　/by/4.0/).