  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 D'Amico 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.
