Our collaboration is responsible for the study of a sample of 72 low mass X-ray binaries (LMXRB) using the INTEGRAL Core Programme data. In this paper we describe the monitoring programme we have started and the current variability and spectral results on a sample of 8 persistently bright LMXRBs hosting a neutron star (Z and Atoll sources). Current results show that among our sample of sources there seems to be no important difference in the variability of Z sources with respect to Atolls and the first colour-colour and hardness intensity diagrams built in the traditional energy bands display the expected patterns. Z sources seem to be harder than the bright Atolls of our sample (above 20 keV) and present no evident cut-off until about 50 keV. A hint of a non-thermal hard tail is seen in Sco X-1 with ISGRI and SPI, similarly to what was previously detected by DAmico et al. (2001) with RXTE. These results, even if preliminary, show the importance of such a programme and the potential underlying it to understand these sources as a class.
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