The present invention is related with the neurobiology and the transgenic animals, more specifically with obtaining a model to study the SCA2 genetic disease. The genome of one mice line has been modified through the introduction of a DNA segment that contains the necessary information for the synthesis of the human ataxin 2. In particular the invention is related with the transgenic mice F066 and the cellular lines able to express the human sca2 gene under the regulation of its self promoter. The F066 transgenic mice reproduce the features of the disease. The homozygous transgenic mouse line for the new gene was obtained through matting. This transgenic line is useful to study the mechanism that produce the disease and also will permit to prove new therapeutics that contributes to minimize the clinical symptoms in the patients.