This paper studies the hypothesis of an inverted-U-shaped relationship between spatial inequality and economic development. The theory of Kuznets (1955) and Williamson (1965) suggests that (spatial) inequality first increases in the process of development, and then decreases. To test this hypothesis I have used a unique panel data set of spatial inequalities in 56 countries at different stages of economic development, covering the period 1980-2009. Parametric and semiparametric regressions are carried out using cross-section and (unbalanced) panel data. The results provide strong support for the existence of an inverted-U. I also find some evidence that spatial inequalities increase again at very high levels of economic development.