There is currently a need for clinical trial methodology that allows formal consideration of toxicity responses. Since a complete evaluation of an experimental therapy addresses both relative efficacy and relative toxicity, general methods for handling bivariate response data are of interest. A procedure for sequentially analysing both efficacy and toxicity data is presented. The procedure is designed to allow early termination due to efficacy results, toxicity results, or both. The method is based on modified marginal sequential analyses, accounting for bivariate correlated responses and multiple analyses over time. The theory is presented in the context of normally distributed responses. Extensions to bivariate failure time data are indicated and an example from a kidney transplant study demonstrates the procedure.