Results of absolute gravity measurements on seven sites of Northern Caucasus region, which form a reference network for control of vertical movements of the region by a gravimetric method, are presented. To spread this network to other parts of the region without carrying out expensive absolute measurements, the technique based on measurement of the gravity increment between the new and reference sites by the high-precision relative gravity meter is developed. Two-years observations showed availability of this technique, nevertheless, for reliable determination of the site vertical movements, the observations on longer time interval are necessary.