In this paper, I want to address the large budget gap that will emerge in Medicare and Medicaid in the decades to come.  In subsequent sections of the paper, I will briefly describe the finances of the programs and some of their major features.  I will then explain the projections done by the U.S. Congressional Budget Office and by the U.S. appointed Board of Trustees of Social Security, Federal Hospital Insurance and Federal Supplementary Medical Insurance Trust Funds.  The final sections of the paper will discuss measures that might be taken to close the budget gap which Medicare and Medicaid create in the context of rising health care costs in the United States.