In minimum-fuel impulsive spacecraft trajectories, long-duration coast arcs between thrust impulses can occur. If the coast time is long enough to allow one or more complete revolutions of the central body, the solution becomes complicated. Lambert's Problem, which is the determination of the orbit, given the terminal radius vectors and the transfer time, has a multiplicity of solutions. For a transfer time long enough to allow N revolutions of the central body there exist 2N + 1 trajectories which satisfy the boundary-value problem. An algorithm based on the classical Lagrange formulation for an elliptic orbit is developed and demonstrated which determines all the trajectories.