Abstract: The models of future earthquake ground motion, besides randomness, have strong fuzziness owing to the ambiguous definitions and norms for evaluation of the intensity degrees and the site soil classification.The forms to express the fuzziness and randomness of the model should be different for problems with different characters and conditions. But mainly there are two kinds of models for earthquake ground motion. The first kind of model is based on the prediction of the fuzzy earthquake intensity and the use of earthquake response spectrum. The other kind of model is a fuzzy random process which at present must be simplified as a random process with fuzzy parameters.Key Words: Fuzzy intensity, Fuzzy predictive intensity, Fuzzy response spectrum, Earthquake ground motion, Fuzzy power spectrum, Fuzzy random process.