Sweden, like many other European countries, has lower employment levels for the foreign-born compared to native-born Swedes. To some extent, this could be due to the country's relatively large intake of refugees. However, few studies have focused entirely on the employment integration of these refugees. In order to fill this gap, we use detailed longitudinal Swedish register data of three arrival cohorts (1998-2000). These data cover the employment of refugees from different countries of origin in Sweden in the first 12 years since their arrival. In line with related work and theoretical considerations and with respect to group characteristics, outmigration, and employment integration over time, we find differences between dissimilar groups of refugees. The findings concerning employment integration decrease to a small degree after rich regression adjustments. Moreover, maybe more surprisingly, we find a very similar result within the main groups of refugees from countries such as Bosnia, Ethiopia, and Eritrea. Women from these groups, in particular, have similar or higher employment probabilities than Swedish-born women after between 5 and 8 years in the country. Overall, each group managed to catch up to a non-negligible, yet varying, degree compared to related empirical evidence from other countries. The role of contextual factors in the refugee sending and receiving countries is highlighted.