We have performed both ac susceptibility and dc magnetization measurements on the diluted magnetic semiconductor Zn 1Ϫx Mn x Te. The measurements clearly indicate spin-glass behavior. For samples with concentrations xϭ0.51 and xϭ0.41, the data for the imaginary part of the complex susceptibility (Љ) were analyzed according to conventional power-law dynamics and good scaling was obtained with the critical exponent values zϭ10Ϯ2 and ϭ1.0Ϯ0.2. These values of z and  are consistent with results obtained in other insulating spin-glass systems with short-range interactions. Because of the presence of significant Dzyaloshinsky-Moriya anisotropy in these materials, an attempt was also made to fit the data using an activated dynamics model. However, the scaling of the Љ data was less satisfactory in this case. Magnetization measurements on the xϭ0.51 sample also showed a spin-glass-like transition. Scaling of the nonlinear magnetization just above the transition gave T c ϭ20.8Ϯ0.2 K, and the critical exponent values ␥ϭ4.0Ϯ1.0 and  ϭ0.8Ϯ0.2. The value of T c obtained from the static magnetization measurements is in good agreement with the value T c ϭ20.7Ϯ0.05 K obtained from the dynamic scaling analysis. Further, the value for the critical exponent ␥ obtained in this work is in fair agreement with values reported for other spin-glass materials. These results represent convincing evidence that diluted magnetic semiconductors are a subset of the class of insulating spin-glass materials with short-range interactions.