Complex permittivity measurements were performed on sorbitol, xylitol, and sorbitol-xylitol mixture in the supercooled liquid state in an extremely wide frequency range from 10 microHz to 500 MHz at temperatures near and above the glass transition temperature. We determined detailed behavior of the relaxation parameters such as relaxation frequency and broadening against temperature not only for the alpha process but also for the beta process above the glass transition temperature, to the best of our knowledge, for the first time. Since supercooled liquids are in the quasi-equilibrium state, the behavior of all the relaxation parameters for the beta process can be compared among the polyols as well as those for the alpha process. The relaxation frequencies of the alpha processes follow the Vogel-Fulcher-Tammann manner and the loci in the Arrhenius diagram are different corresponding to the difference of the glass transition temperatures. On the other hand, the relaxation frequencies of the beta processes, which are often called as the Johari-Goldstein processes, follow the Arrhenius-type temperature dependence. The relaxation parameters for the beta process are quite similar among the polyols at temperatures below the alphabeta merging temperature, T(M). However, they show anomalous behavior near T(M), which depends on the molecular size of materials. These results suggest that the origin of the beta process is essentially the same among the polyols.