Most assessments of immigrant adaptation to the institutions of Australian society and its labour market are cautiously optimistic. While immigrants, especially those from non‐English‐speaking background, do suffer initial economic disadvantage, their position improves with the passage of time. There is, moreover, little evidence that the Australian‐born children of immigrants suffer continuing disadvantage. These optimistic assessments are based mainly on evidence from the period preceding the emergence of sustained, high unemployment that prevailed during the 1980s and into the 1990s. I use pooled data from the Public Use Samples for the 1981 and 1991 censuses of Australia to assess changes in relative advantage and disadvantage over time. The data show that, over this period, some immigrant groups fared worse with respect to the risk of unemployment. As for their chances of entering the highest occupational class, they benefited along with other Australians from the expansion of professional and managerial jobs, an outcome exaggerated by the loss of many manufacturing jobs due to cuts in tariff protection and trade liberalisation (policies that also increased measured unemployment and hidden unemployment). With respect to occupational earnings, workers suffered a general decline in real weekly incomes, immigrants and native‐born alike. However, many immigrant workers continued to earn significantly less than comparable native‐born workers, with little evidence of economic convergence over the course of their working lives.