This paper introduces the concept of almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions in bitopological spaces. The authors investigate several characterizations of such multifunctions. The paper begins with an introduction to the concept of continuity in bitopological spaces, highlighting various generalizations and related concepts such as ($\Lambda, sp$)-open sets, quasi-continuous functions, and other types of continuity. It then presents preliminary definitions and properties of bitopological spaces, including ($\tau_{1}, \tau_{2}$)-open sets, ($\tau_{1}, \tau_{2}$)-closed sets, and ($\tau_{1}, \tau_{2}$)-s-open and ($\tau_{1}, \tau_{2}$)-s-closed sets. The main contribution of the paper is the introduction of the concept of almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions. The authors define this concept and provide several equivalent characterizations. They prove that a multifunction is almost quasi ($\tau_{1}, \tau_{2}$)-continuous at a point if, for every $\sigma_{1}\sigma_{2}$-open sets $V_{1}, V_{2}$ of Y such that $F(x) \in V_{1}^{+} \cap V_{2}^{-}$, there exists a ($\tau_{1}, \tau_{2}$)-s-open set U of X containing x such that $F(U) \subseteq (\sigma_{1}, \sigma_{2})$-sCl($V_{1}$) and $(\sigma_{1}, \sigma_{2})$-sCl($V_{2}$) $\cap$ F(z) $\neq$ $\emptyset$ for every z $\in$ U. The authors also show that several other properties are equivalent to this definition, including the condition that $F^{+}(V_{1}) \cap F^{-}(V_{2})$ is ($\tau_{1}, \tau_{2}$)-s-open in X for every ($\sigma_{1}, \sigma_{2}$)-r-open sets $V_{1}, V_{2}$ of Y. The paper concludes with several theorems that establish the equivalence of various properties related to almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions.This paper introduces the concept of almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions in bitopological spaces. The authors investigate several characterizations of such multifunctions. The paper begins with an introduction to the concept of continuity in bitopological spaces, highlighting various generalizations and related concepts such as ($\Lambda, sp$)-open sets, quasi-continuous functions, and other types of continuity. It then presents preliminary definitions and properties of bitopological spaces, including ($\tau_{1}, \tau_{2}$)-open sets, ($\tau_{1}, \tau_{2}$)-closed sets, and ($\tau_{1}, \tau_{2}$)-s-open and ($\tau_{1}, \tau_{2}$)-s-closed sets. The main contribution of the paper is the introduction of the concept of almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions. The authors define this concept and provide several equivalent characterizations. They prove that a multifunction is almost quasi ($\tau_{1}, \tau_{2}$)-continuous at a point if, for every $\sigma_{1}\sigma_{2}$-open sets $V_{1}, V_{2}$ of Y such that $F(x) \in V_{1}^{+} \cap V_{2}^{-}$, there exists a ($\tau_{1}, \tau_{2}$)-s-open set U of X containing x such that $F(U) \subseteq (\sigma_{1}, \sigma_{2})$-sCl($V_{1}$) and $(\sigma_{1}, \sigma_{2})$-sCl($V_{2}$) $\cap$ F(z) $\neq$ $\emptyset$ for every z $\in$ U. The authors also show that several other properties are equivalent to this definition, including the condition that $F^{+}(V_{1}) \cap F^{-}(V_{2})$ is ($\tau_{1}, \tau_{2}$)-s-open in X for every ($\sigma_{1}, \sigma_{2}$)-r-open sets $V_{1}, V_{2}$ of Y. The paper concludes with several theorems that establish the equivalence of various properties related to almost quasi ($\tau_{1}, \tau_{2}$)-continuous multifunctions.