We reportRXTEresults of spectral analyses of three (Sco X-1, GX349+2,and Cyg X-2) out of the 6 known Z sources. No hard X-ray tails were found for Cyg X-2 (<8.4×10−5 photons cm−2 s−1,50–100 keV, 3&sgr;) and for GX349+2(<7.9×10−5photons cm−2 s−1,50–100 keV, 3&sgr;). For Sco X-1 a variable hard X-ray tail (with an average flux of2.0×10−3 photons cm−2 s−1,50–100 keV) has already been reported. We compare our results to reported detections of a hard component in the spectrum of Cyg X-2 and GX349+2.We argue that, taking into account all the results on detections of hard X-ray tails in Sco X-1 and GX349+2,the appearance of such a component is correlated with the brightness of the thermal component. ©2001 American Institute of Physics.