The recombination rates in meioses of females and males are often different. Some genes that affect development and behavior in mammals are known to be imprinted, and >1% of all mammalian genes are believed to be imprinted. When the gene is imprinted and the recombination fractions are sex specific, the conventional transmission disequilibrium test (TDT) is shown to be still valid for testing for linkage. The power function of the TDT is derived, and the effect of the degree of imprinting on the power of the TDT is investigated. It is learned that imprinting has little effect on the power when the female and male recombination rates are equal. On the basis of case-parents trios, the transmissions from the heterozygous fathers/mothers to their affected children are separated as paternal and maternal, and two TDT-like statistics, TDT(p) and TDT(m), are consequently constructed. It is found that the TDT(p) possesses a higher power than the TDT for maternal imprinting genes, and the TDT(m) is more powerful than the TDT for paternal imprinting genes. On the basis of the parent-of-origin effects test statistic (POET), a novel statistic, TDT incorporating imprinting (TDTI) is proposed to test for linkage in the presence of linkage disequilibrium, which is shown to be more powerful than the TDT when parent-of-origin effects are significant but slightly less powerful than the TDT when parent-of-origin effects are negligible. The validity of the TDT and TDTI is assessed by simulation. The power approximation formulas for the TDT and TDTI are derived and the simulation results show that they are accurate. The simulation study on power comparison shows that the TDTI outperforms the TDT for imprinted genes. The improvement can be substantial in the case of complete paternal/maternal imprinting.