  One of the most fundamental results in graph theory is Mantel's theorem which
determines the maximum number of edges in a triangle-free graph of order $n$.
Recently a colorful variant of this problem has been solved. In such a variant
we consider $c$ graphs on a common vertex set, thinking of each graph as edges
in a distinct color, and want to determine the smallest number of edges in each
color which guarantees existence of a rainbow triangle. Here, we solve the
analogous problem for directed graphs without rainbow triangles, either
directed or transitive, for any number of colors. The constructions and proofs
essentially differ for $c=3$ and $c \geq 4$ and the type of the forbidden
triangle. Additionally, we also solve the analogous problem in the setting of
oriented graphs.
