In some developing nations, many end-stage renal disease (ESRD) patients die because the costs of kidney transplantation and dialysis are beyond the reach of most citizens. In this paper, we analyze two proposals for extending kidney exchange to include patients in countries in which transplantation is unavailable to them. First, we analyze a recently proposed concept, Global Kidney Exchange, in which a U.S. health authority invites patients with financial restrictions who have willing donors to come to the United States to exchange their donor’s kidney with an immunologically incompatible American patient-donor pair and to receive a transplant utilizing the incompatible American donor’s kidney for free. We create a dynamic model of this proposal and show that this proposal can be self-financing in the long run. Our analysis shows that, under plausible assumptions, the proposal remains self-financing even when the average dialysis cost of American patients declines below the cost of surgery (as waiting times for transplant are shortened by the increased availability of transplants). The ability of such a program to benefit foreign patient-donor pairs would be limited only by the number of American pairs with whom they could be matched, which is in the single digit thousands. We also introduce a new proposal, the Non-Directed Donor proposal, which would relax this limit, by including foreign pairs that could be associated with a non-directed donor who could donate a kidney to a patient on the U.S. waiting list for deceased donors. The ability of such a program to benefit foreign patient-donor pairs associated with non-directed donors would be limited only by the total number of American patients with ESRD, which includes at least the hundred thousand currently on the deceased donor waiting list and perhaps 50,000 per year in the steady state