In this paper, we discuss an upper bound for exponents of loopless asymmetric two-colored digraphs. If \( D \) is an asymmetric primitive two-colored digraph on \( n \) vertices, we show that \( \text{exp}(D) \leq 3n^2 + 2n – 2 \). For an asymmetric two-colored digraph \( D \) which contains a primitive two-colored cycle of length \( s \leq n \), we show its exponent is at most \( \frac{s^2 – 1}{2} + (s + 1)(n – s) \). We characterize such two-colored digraphs whose exponents equal \( \frac{s^2 – 1}{2} + (s + 1)(n – s) \) and show that the largest exponent of an asymmetric two-colored digraph lies in the interval \( \left[\frac{n^2 – 1}{2}, 3n^2 + 2n – 2\right] \) when \( n \) is odd, or \( \left[\frac{n^2}{2}, 3n^2 + 2n – 2\right] \) otherwise.