We look at migration flows from 8 Central and Eastern European Countries (CEECs) to 5 Nordic countries over the years 1985 - 2005 and we can exploit a natural experiment that arose from the fact that while Sweden opened its labour market from the day one of the 2004 EU enlargement, the other Nordic countries chose a transition period in relation to the "new" EU members. We employ a differences-in-differences estimator in our analysis. The results show that the estimated effect of the opening of Swedish labour market in 2004 on migration is insignificantly different from zero. Further, we are interested in the overall effect of the "EU entry" on migration. Therefore we look at migration flows from CEECs during the first round EU enlargement towards CEECs in 2004 and compare them with migration flows from Bulgaria and Romania. We again used a DD estimator in our analysis. The estimated effect is positive and significant in all model specifications.