A mathematical model has been developed using the space engagement theory and the differential geometry for the line contact of noninvolute beveloid gears with intersecting axes with their tooth profile equations and engagement equations established for the first time and their meshing theory analysed. It can be seen from the fact that the tooth profile equation finally derived is no longer a standard involute helicoid and standard involute beveloid gears with intersecting axes have no way to satisfy the line contact requirement. However, the noninvdute beveloid gears derived in this paper satisfy the line contact requirement very well. All these work will inevitably facilitate further investigations into gear tooth generation, stiffness, backlash and efficiency of transmission.