We discuss the analysis of non-inferiority trials based on a multi-armed design with multiple correlated endpoints. We consider five different scenarios: (1) global non-inferiority; (2) non-inferiority for subsets of comparisons; (3) global non-inferiority for a treatment group; (4) global non-inferiority for an endpoint; and (5) local non-inferiority. We describe and compare related approaches, which are based on the union-intersection and intersection-union test principles – alone and in combination. Because non-inferiority thresholds for many differently scaled endpoints are rarely available in practice, the approaches described focus on the estimation of simultaneous confidence limits and their post hoc interpretation on non-inferiority. We discuss and demonstrate pros and cons by means of a real data example. Copyright © 2012 John Wiley & Sons, Ltd.