Association studies of genetic markers with disease play a critical role in the dissection of genetically complex traits because they are relatively easy to conduct and are useful for fine-scale mapping of genetic traits. The advantage of family-based controls has recently received much attention because spurious associations caused by population structure can be controlled for, and marker genotype information on diseased cases and their parents can be used to test the compound hypothesis of both linkage and linkage disequilibrium. However, debate still exists regarding the statistical methods of analysis. Herein are presented statistical methods to test for linkage (in the presence of linkage disequilibrium) between multiallelic genetic markers and disease when diseased subjects (cases) and their parents are sampled. Theoretical considerations for the development of general statistical tests are presented as well as asymptotic formulas to compute their power when planning a study. Furthermore, simulation results for nine specific statistics are used to contrast the power of these methods under different genetic mechanisms leading to disease (dominant vs. recessive, one vs. two high-risk alleles). These results demonstrate substantial gains in power for specific statistical tests designed to detect specified genetic mechanisms. However, without a priori knowledge of the likely genetic mechanism, it is desirable to rely on a fairly robust statistical method, robust so that power is not drastically lost when either dominant or recessive mechanisms are acting, and when either one or more than one marker alleles are associated with disease. Based on both theoretical and simulation results, a general score statistic, which generalizes the transmission/disequilibrium test, tends to offer sufficient power for a variety of genetic mechanisms, so that it is worth considering for broad use in studies which use genetic marker information from both diseased cases and their parents.