Nate Dogg's teenage sons are following in their father's footsteps -- telling TMZ, they're currently in the process of launching their own music careers ... in fact, they even plan to work with their "Uncle Snoop."

15-year-old Naijiel and 18-year-old Lil Nate revealed their game plan in L.A. yesterday ... and gave us a sample of the goods to boot.

Not bad.