Adult stem cells obtained from the carotid body, characterized in that they are positive for the phenotypic marker GFAP (glial fibrillary acidic protein) and negative for the phenotypic markers TH (tyrosine hydroxylase) and nestin, are described. These stem cells can undergo proliferation, self-renewal and differentiation to progenitor cells and differentiated cells. Said stem cells, progenitor cells and differentiated cells, expanded by any method, can be used in the treatment of neurodegenerative diseases such as Alzheimers disease or Parkinsons disease.