In the open unit disk $\{\varsigma\in\mathbb{C}:|\varsigma| <1\}$, two subclasses of bi-univalent functions related to Horadam polynomials are presented and examined in this paper. For functions belonging to the recently established classes, we obtain the estimates of the first two coefficients. Furthermore, an estimate of the Fekete-Szegö problem is provided for functions in these classes. We also provide some observations and draw relevant connections to earlier research.