A couple of conjugate screw surfaces, which create a three-member mechanism with a higher kinematic pair, constitutes an important part of mechanical systems. One of these surfaces is created as an envelope of the second surface. In an ideal arrangement surface axes are parallel and the contact between both surfaces is curvilinear. After displacement of the surface axes, which is induced in technical equipments by force and heat loading, the original parallel arrangement of the surface axes is changed into an incorrect, spatial or alternatively parallel displaced, position. Consequently the original curvilinear contact changes into a contact at a point. This change is significant from the view of contact analysis. Determination of the contact point of conjugate surfaces, which are in the incorrect position, based on the kinematic way is presented in this contribution.