The　purpose　of　this　paper　is　to　propose　a　pair　of　external　and　internal　spiral　bevel　gears　with　double　circular-arc　in　the　nutation　drive.　Based　on　the　movement　of　nutation,　this　paper　develops　equations　of　the　tooth　profiles　for　the　gear　set,　leading　to　the　mathematical　modeling　of　the　spiral　bevel　gear　with　a　constant　helical　angle　gear　alignment　curve,　enabling　the　tooth　surface　to　be　generated,　and　permitting　the　theoretical　contacting　lines　to　be　produced　in　light　of　the　meshing　function.　Simulation　and　verification　are　carried　out　to　prove　the　mathematical　equations.　Numerical　control　(NC)　simulation　of　machining　the　external　and　internal　double　circular-arc　spiral　bevel　gears　is　developed,　and　the　spiral　gears　were　manufactured　on　a　NC　milling　machine.　The　prototype　of　the　nutation　drive　is　illustrated　in　the　case　study　at　the　end　of　this　paper.　[DOI:　10.1115/1.4001003]