The stability of the network of the Ukrainian SLR stations «Simeiz», «Katzively», «Golosiiv—Kiev», «Lviv» are investigated on the basis of the results of reducing the LAGEOS-1 and LAGEOS-2 observations from 5 January 1989 to 11 November 2004. The stability of coordinate determination for every station are estimated. The factors influencing on the stability of the network are outlined.