Abstract. Title of the paper: The Robustness of BLUP and EBLUP The expectations of BLP and BLUP used as estimator for fixed effects and as predictor for random effects were investigated concerning the property "unbiasedness". Different aspects of robustness research on prediction procedures are discussed. The robustness of BLUP and EBLUP was investigated with respect to the distribution ofthe random components of the model, the degree of balancedness of the experimental design, influence of the variance components ratio and different variance component estimators used in EBLUP(2) on the bases of a Computer Simulation in the random one-way model. Criteria used for the evaluation were the mean squared error (MSE) and the selection gain. Besides, an idea of the overestimation of the accuracy of EBLUP by the naive MSE approximation based on the MSE formulas of BLUP with variance component estimations instead of unknown parameters is given.