Abstract: This paper describes the method of the differential neighborhood used for investigation of the local conjugate problem of the gear tooth surfaces. By the osculating paraboloid principle, we get all the calculating formulas far setting the hypoid generator with the modified roll. As a result these formulas can be used to make both the computer program and manual calculation sheets for the spiral bevel gear tooth cutting jobs. Today, we have had a variety of the formula calculating the conjugate normal curvature of the surfaces by the relative motion parameters[2][3][10][11][15]. For the conveniences of the engineering, this paper has given another strict proof to the adopted Baxter's formula by using a conventional method and complemented the indispensable general formula of acceleration of relative motion in the conjugate movment between the surfaces.