Measurement invariance is a necessary precondition for meaningful cross-country comparisons, and three levels have been differentiated: configural, metric, and scalar. Unfortunately, establishing the most stringent form, i.e., scalar measurement invariance, across groups is difficult. Recently, Muthén and Asparouhov proposed testing for approximate rather than exact measurement invariance as this may be sufficient for meaningful comparisons. Following their strategy, the results of cross-country approximate measurement invariance tests of the PVQ-21 scale to measure values in the European Social Survey (ESS) are presented (N = 274,447 respondents from 15 countries participating in all six rounds). Applying the new approximate method for the test of measurement invariance allows both using more moderate constraints of approximate equality of parameters across groups and exploring the extent of noninvariance. Approximate measurement invariance was established in almost all rounds for two higher-order values: openness to change and self-enhancement. In the case of the two other higher-order values, self-transcendence and conservation, approximate measurement invariance was established across a subset of countries.