Roughly half of Medicare beneficiaries under age sixty-five are also eligible for Medicaid. These "dual eligibles" have been the subject of much research because of their low income and poor health status. Previous studies suggest that some states seek to shift costly health care services for this group out of state-run Medicaid programs and into the federally funded Medicare program--for example, replacing nursing home care with hospital care. Using state-level data on dual eligibles under age sixty-five, we found support for this hypothesis. In states with below-average per capita Medicaid spending, corresponding Medicare spending was above average. These state-level estimates also revealed a nearly threefold difference in total--Medicare plus Medicaid-price--adjusted spending per person, ranging from $16,309 in Georgia to $43,587 in New York. Such large variations among people with serious diseases suggest inefficiency. Some states may be spending too little for Medicaid, meaning that some patients' needs are not being met, or some states may be spending too much, meaning that more services are being provided than needed. Such inefficiency exposes patients to unnecessary risk, drives costs up unnecessarily, and highlights the large potential gains arising from improved care coordination for dual eligibles.