Race and ethnicity responses can change over time and across contexts – a component of population change not usually taken into account. To what extent do race and/or Hispanic origin responses change? Is change more common to/from some race/ethnic groups than others? Does the propensity to change responses vary by characteristics of the individual? To what extent do these changes affect researchers? We use internal Census Bureau data from the 2000 and 2010 censuses in which individuals’ responses have been linked across years. Approximately 9.8 million people (about 6 percent) in our large, non-representative linked data have a different race and/or Hispanic origin response in 2010 than they did in 2000. Several groups experienced considerable fluidity in racial identification: American Indians and Alaska Natives, Native Hawaiians and Other Pacific Islanders, and multiple-race response groups, as well as Hispanics when reporting a race. In contrast, race and ethnic responses for single-race non-Hispanic whites, blacks, and Asians were relatively consistent over the decade, as were ethnicity responses by Hispanics. People who change their race and/or Hispanic origin response(s) are doing so in a wide variety of ways, as anticipated by previous research. For example, people’s responses change from multiple races to a single race, from a single race to multiple races, from one single race to another, and some people add or drop a Hispanic response. The inflow of people to each race/Hispanic group is in many cases similar in size to the outflow from the same group, such that cross-sectional data would show a small net change. We find response changes across ages, sexes, regions, and response modes, with variation across groups. Researchers should consider the implications of changing race and Hispanic origin responses when conducting analyses and interpreting results.