  We conjecture that every oriented graph $G$ on $n$ vertices with $\delta ^+
(G) , \delta ^- (G) \geq 5n/12$ contains the square of a Hamilton cycle. We
also give a conjectural bound on the minimum semidegree which ensures a perfect
packing of transitive triangles in an oriented graph. A link between Ramsey
numbers and perfect packings of transitive tournaments is also considered.
