We present an analysis of the spectral and timing properties observed in X-rays from neutron star binary GX~3+1. We analyze all observations of this source obtained with the RXTE and BeppoSAX satellites. We find that the X-ray broad-band energy spectra during these spectral transitions can be adequately reproduced by a composition of a low-temperature blackbody component, a Comptonized component (COMPTB) and Gaussian component. We argue that the electron temperature kT_e of the Compton cloud

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... otonically increases from 2.3 keV to 4.5 keV, when GX~3+1 makes a spectral transition. Using a disk seed photon normalization of COMPTB, which is proportional to mass accretion rate, we find that the photon power-law index Gamma is almost constant (Gamma=2.00+/- 0.02) when mass accretion rate changes by factor 4. We interpret this quasi-stability of the index Gamma and a particular form of the spectrum in the framework of a model in which the energy release in the transition layer located between the accretion disk and neutron star surface dominates that in the disk. Moreover, this index stability effect now established for GX~3+1 was previously found in the atoll source 4U~1728-34 and suggested for a number of other LMXB NS binaries (see Farinelli & Titarchuk). This intrinsic behavior of neutron stars, in particular for atoll sources, is fundamentally different from that seen in black hole binary sources where the index monotonically increases during spectral transition from the low state to the high state and then finally saturates at high values of mass accretion rate.