Abstract. Within the Cornwall -Jackiw -Tomboulis (CJT) approach a general formalism is established for the study of asymmetric nuclear matter (ANM) described by the Nambu-Jona-Lasinio (NJL) model. Restricting to the double-bubble approximation (DBA)we determine the bulk properties of ANM, in particular, the density dependence of the nuclear symmetry energy, which is in good agreement with data of recent analyses.