This study examined the effect of Asian nativity and duration of residence in Australia on the odds of reporting a chronic health condition (cancer, respiratory problems, cardiovascular disease (CVD) and diabetes mellitus). Data were from waves 3, 7 and 9 of the Household Income and Labour Dynamics in Australia (HILDA) longitudinal survey, and multi-level group-mean-centred logistic regression models were used for the analysis. After covariate adjustment, Asian immigrants were less likely to report cancer and respiratory problem compared with native-born Australians. While there was no significant difference in reporting CVD, they were more likely to report diabetes than native-born people. Asian immigrants maintained their health advantage with respect to cancer regardless of duration of residence. However, after 20 years of stay, Asian immigrants lost their earlier advantage and were not significantly different from native-born people in terms of reporting a respiratory problem. In contrast, Asian immigrants were not measurably different from native-born Australians in reporting diabetes if their length of stay in Australia was less than 20 years, but became disadvantaged after staying for 20 years or longer. There was no measurable difference in the odds of reporting CVD between Asian immigrants and native-born Australians for any duration of residence. On the whole this study found that health advantage, existence of healthy immigrant effect and subsequent erosion of it with increasing duration of residence among Asian immigrants depends upon the chronic health condition.