We discuss methods for early efficacy evaluation in group-sequential clinical trials that compare two interventions using two time-to-event outcomes, where the two time-to-event outcomes have a time-dependent association generated by two bivariate exponential distributions under three censoring schemes, when: (i) both events are non-fatal, (ii) one event is fatal, and (iii) both events are fatal. We consider two inferential goals, i.e., to evaluate if a test intervention is superior to a control intervention on: (1) both outcomes (multiple co-primary endpoints) or (2) on at least one outcome (multiple primary endpoints). One complex challenge in these trials is how to allocate alpha to each interim analysis to control the Type I rate, as information for the outcomes may not accrue at the same rate and requires different information times. We consider several strategies for alpha spending and evaluate the behavior of the Type I error rate. We investigate the operating characteristics of the strategies in terms of the Type I error, power and sample sizes, and provide guidance on constructing efficient group-sequential designs in clinical trials with two time-to-event outcomes.