Dynamic mechanical behavior of a series of partially hydrogenated polystyrenes with various degrees of hydrogenation has been investigated. The primary relaxation process ascribed to glass transition shifts to higher temperatures and broadens with increasing degree of hydrogenation. There exist two secondary dispersions in a temperature range from 110 to 250 K. The frequency dependence of these relaxation processes and the molecular dynamics simulation suggest that the secondary relaxations are associated with the chair-chair flipping and oscillatory rotation of the cyclohexyl group.