<p>This paper studies time-inconsistent two-person non-zero-sum differential games under an open-loop framework. We introduce the equilibrium value function and quasi-variational problems, equilibrium two-point boundary value problems, and equilibrium Hamilton–Jacobi–Bellman (HJB) equations with non-intrinsic function. It is established that the existence of a Nash equilibrium is equivalent to the solvability of the quasi-variational problem. We prove that the equilibrium value function serves as a solution to the equilibrium HJB equation, and discuss the relationship between the equilibrium value function and the adjoint variables in the two-point boundary value problem.</p>