We study bilateral trading between two bidders in a divisible double auction. The bidders (1) submit demand schedules, (2) have interdependent and linearly decreasing marginal values, and (3) can be asymmetric. Existing models of divisible double auctions typically require at least three bidders for the existence of linear equilibria. In this paper, we characterize a family of nonlinear ex post equilibria with two bidders, implicitly given by a solution to an algebraic equation.  We show that the equilibrium amount of trading is strictly less than that in the ex post efficient allocation.  If marginal values do not decrease with quantity, we solve the family of ex post equilibria in closed form.  Our theory of bilateral trading differs from the bargaining literature and can serve as a tractable building block to model dynamic trading in decentralized markets.