The description of the jobs is a very important issue for the scheduling and management of Grid jobs. Since there are a lot of different languages for describing Grid jobs, the GGF have presented the Job Submission Description Language (JSDL) to standardize the job submission language. We believe that the JSDL is a good solution but it has some deficiencies regarding the parallelism issues. In this paper we propose an extension of the JSDL to specify the parallelism details of Grid jobs. This extension is proposed in general terms for supporting current multilevel parallel applications and incoming approaches in parallel programming models. We also discus the suitability of the multilevel parallel programming models for Grids, in particular the MPI+OpenMP since our project, the eNANOS project, is based on this hybrid programming model.