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We present an analysis of the spectral and timing properties of X-ray radiation from accreting neutron star source GX340+0 during its evolution when the electron temperature of the transition layer (TL) kTe monotonically decreases from 21 to 3 keV. We analyze episodes observed with BeppoSAX and RXTE. We reveal that the X-ray broadband energy spectra during all spectral states can be reproduced by a physical model composed of a soft Blackbody component and two Comptonized components (both due to the presence of the TL that upscatters both seed photons of T_s1≤1 keV coming from the disk (first component Comptb1), and seed photons of temperature T_{s2}≤1.5 keV coming from the neutron star (second component Comptb2) and the iron-line (Gaussian) component. Spectral analysis using this model indicates that the photon power-law indices Gamma_com1 and Gamma_{com2} of the Comptonized components are almost constant, Gamma_{com1} and Gamma_{com2} 2 when kTe changes from 3 to 21 keV along the Z-track. We interpret the detected quasi-stability of the indices of Comptonized components to be near a value of 2. Furthermore, this index stability now found for the Comptonized spectral components of Z-source GX340+0 is similar to that previously established in the atoll sources 4U1728-34, 4U1820-30 and GX3+1, and earlier proposed for a number of X-ray neutron stars (NSs). This behavior of NSs both for atoll and Z-sources is essentially different from that observed in black hole binaries where Gamma_{com} increases during a spectral evolution from the low state to the high state and ultimately saturates at a high mass accretion rate