Trimethylamine N-oxide (TMAO) stabilizes protein structures, whereas urea destabilizes proteins, and their opposing effects can be counteracted at a 1:2 ratio of TMAO to urea. To investigate how they affect solution dynamics, molecular dynamics simulations have been carried out for aqueous solutions of TMAO and urea at different concentrations. In the binary solutions, urea mainly slows the diffusion of waters that are hydrogen bonded to it (i.e., hydration water), whereas TMAO dramatically slows the diffusion of both hydration water and bulk water because of long-lived TMAO-water hydrogen bonds. In the ternary solutions, because TMAO decreases the diffusion rate of bulk water, the lifetimes of not only water- water but also urea-water hydrogen bonds increase. In addition, the constant forming and breaking of short lifetime hydrogen bonds between urea and water appears to impart energy into the bulk, whereas the long lifetime hydrogen bonds between TMAO and water slows down the bulk, resulting in the compensating effects on bulk water in the ternary solution. This suggests that the counteracting effects of TMAO on urea denaturation may be both to make longer lived hydrogen bonds to water and to counter the energizing effects of urea on bulk water.