Synthesis of tooth surfaces of spiral Hypoid and Bevel Gears ..Gleason-Formate” is considered. The tooth surfaces of the pinio n are cut by generating with an imaginary conical generating gear. Contact conditions in the pitch point — the amount of mismatch and the toothcontact pattern—are satisfied by the solving of a non-linear system ot equations. Formulas lor calculation of the initial approximate solution of the system are obtained.