The article studies over-time changes in public attitudes towards asylum seekers, from a cross-national comparative perspective. The article applies the 'hierarchical age-period-cohort' model to data from the European Social Survey collected in 17 European countries. The findings demonstrate that cross-cohort variations play a negligible role in the over-time changes in attitudes towards asylum seekers in Europe; and that most of these over-time changes can be attributed to period-related effect. The main findings reveal that not only exposure to an actual high inflow of asylum seekers (i.e. living in a country with an especially high inflow of asylum seekers) is associated with exclusionary attitudes towards asylum seekers, but also exposure to the potential of such an inflow (i.e. living in a country bordering countries with a high inflow of asylum seekers).