We discuss several new powerful family-based approaches for testing genetic association when the traits are obtained from longitudinal or repeated measurement studies. The popular approach FBAT-PC is based on a linear combination of the individual traits. We propose a one-sided modification, FBAT-PCM, which has a closed-form expression and is always more powerful. We also present two approaches FBAT-LC and FBAT-LCC based on linear combination of the univariate test statistics. Furthermore, all three approaches are shown to be unified to a general form. Through simulation studies, we compare the power of these tests under different models of genetic effect sizes. Compared to original FBAT-PC, our modification achieves a power gain of up to 50%. In addition, all three new approaches gain substantial power compared to the ordinary approach of Bonferroni correction, with the relative performance depending upon the underlying model. Application of these approaches for testing an association between Body Mass Index and a previously reported candidate SNP confirms our results.