In clinical trials, multiple endpoints are frequently used to evaluate the treatment effect of new drugs and vaccines. Support for product label may be based on multiple primary endpoints and additionally, multiple secondary endpoints. Therefore, it is important to recognize and appropriately address the multiplicity issue associated with the multiple comparisons in order to control the overall Type I error rate. In this talk, we will discuss and compare several methods for multiplicity adjustment within the family of multiple primary endpoints and among families of multiple primary and secondary endpoints. Power and family-wise Type I error rate of various methods including gate-keeping strategies will be assessed. Examples will be used for illustration and discussion. Finally, recommendations about these multiplicity adjustment methods will be made for practical use.