Several family-based approaches for testing genetic association with traits obtained from longitudinal or repeated measurement studies have been previously proposed. These approaches utilize the multivariate data more efficiently by using estimated optimal weights to combine univariate tests. We show that these FBAT approaches are still robust against hidden population stratification, but their power can be heavily affected since the estimated weights might provide poor approximation of the true theoretical optimal weights with the presence of population stratification. We introduce a permutation-based approach FBAT-MinP and an equal combination approach FBAT-EW, both of which do not involve the use of estimated weights. Through simulation studies, FBAT-MinP and FBAT-EW are shown to be powerful even in the presence of population stratification, when other approaches may substantially lose their power. An application of these approaches to the Childhood Asthma Management Program (CAMP) study data for testing an association between body mass index and a previously reported candidate SNP is given as an example.