This paper studies the equilibrium outcomes of a duopoly game under double endogenous choices, i.e. both the strategic variables (price or quantity) and the move-timing (first-mover or second-mover) are chosen endogenously. It is showed that whether the strategic variables are chosen before or after endogenous timing the equilibrium outcomes are identical. The equilibrium outcomes are quantity competitions with three kinds of move-orders, i.e. one simultaneous-move game and two sequential-move games with both leader-follower configurations.