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.　©　2024　The　Authors