We analyse the dynamics of employment assimilation of first-generation immigrant men in Sweden using a high-quality, register-based panel data set. It is discussed that when there are significant differences between employment status persistence of immigrants and natives, the standard static assimilation model produces biased predictions for the relative labour market outcomes for immigrants. We find significant persistence of employment status which differs between immigrants and natives, and also across immigrant groups. The static assimilation model overestimates (underestimates) the short-run (long-run) marginal assimilation rates. We find 10-15 percentage points lower initial employment probability disadvantage but the years to assimilation are 5-10 years longer compared to the standard static assimilation model.