Using a proportional hazard model with multiple exits, this paper analyzes whether immigrants' unemployment spells differ from natives', and if so, how the difference vary with time spent in Sweden and across immigrant cohorts. A unique data set taken from the Swedish unemployment registers is used. The data set covers the period 1991 to 1996, a period of substantial increases in both unemployment rates as well as in immigration. The estimates from the hazard model suggests that a substantial proportion of the observed difference in unemployment spells between natives and immigrants can be explained by differences in accumulated human capital and unemployment compensation. This is especially true regarding the difference between natives and refugees.