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This paper investigates the role that pre-immigration skills play in immigrants job-finding processes in Germany. We first show theoretically that the job-finding rate for the high-skilled depends on which jobs they are prepared to take up: if they are only willing to take up skilled jobs (ex post segmented matching), they might actually need longer than the low-skilled to find a job. If they are prepared to accept both unskilled as well as skilled jobs (cross-skill matching), then their expected time to find a job is lower compared to that of the low-skilled. Allowing for on-the-job search can lead to high-skilled finding skilled jobs even faster. We then provide empirical evidence by studying the labour-market integration process of Ethnic Germans, one of the largest immigration groups in Germany, using novel German administrative data. Applying proportional hazard models, our estimates generally support the theoretical predictions: if the high-skilled only search for skilled jobs, the likelihood of finding a job is about 50% lower compared to the low-skilled. In case of cross-skill matching, the job finding rate of the high- and low-skilled does not differ significantly. Furthermore, using a timing-of-events model, we find evidence that low-skilled jobs serve as a stepping stone for high-skilled to find skilled employment.