In this paper a mathematical model for determination of intersecting curve between two surfaces of revolution was formed. A generating meridian and an axis of revolution give each surface of revolution where meridian and axis lie in one plane. Projecting rays are orthographic to the plane defined by the axis and the meridian, and in this case this meridian is one contour generatrix of the surface. Based on combined transformation [4] (translation, rotation and reflection) the other contour generatrix is determined, and the axis of rotation is coincident with axis of symmetry. Using purely descriptive geometric method of auxiliary spheres the intersecting curve between two surfaces of revolution can be easily determined. This method is used when axes of surfaces meet each other [1]. The centre of all auxiliary spheres is intersecting point of these axes. Each sphere intersects both surfaces at two parallel circles. These four circles are on their common sphere so that circles either meeting each other or not. Circles, which intersect each other, define real points of the space curve. Spheres with minimal and maximal diameter, which define particular points of the intersecting curve, are determined as well.