A positioning system used in assembling a scroll-type fluid machine exerts a horizontal thrust on a stationary scroll in a direction opposite to a direction in which an eccentric shaft end portion formed at one end of a rotary shaft is oriented while turning the rotary shaft, and determines an orbital path of the stationary scroll by measuring horizontal displacements thereof. While exerting the horizontal thrust, the positioning system incrementally presses the stationary scroll against a guide frame until a stable orbital path of the stationary scroll is obtained. When the orbital path is judged to be stable, the positioning system determines a fixing point on which the stationary scroll should be fixedly centered with respect to the guide frame, so that a scroll wrap of the stationary scroll and a scroll wrap of an orbiting scroll are correctly intermeshed, forming a series of pockets therebetween.