Complex dielectric spectra of diethylsulfoxide (DESO)/water mixtures at 25 C over the entire concentration range of DESO, in the frequency range 0.2 / GHz 89 have been measured. In general, a description of the complex permittivity spectra requires a consideration of different types of relaxation processes depending upon DESO concentration. For the lower DESO concentration range the relaxation contribution to the spectrum is described by two Debye terms, whereas for higher concentration three Debye terms are used. For both at mol fraction equals to 0.9 and pure DESO as well Cole-Davidson type is valid. In addition, the data on the dimethylsulfoxide (DMSO)/water system obtained in this work well agree with those known from literature. The concentration dependent excess dielectric constant, excess inverse relaxation time and Kirkwood correlation factor of the mixtures have been determined.