  We show an analysis of the spectral and timing properties of X-ray radiation
from Z-source during its evolutions when the electron temperature of the
Transition Layer (TL) kT_e monotonically decreases from 21 to 3 keV. We analyze
episodes observed with the BeppoSAX and Rossi X-ray Timing Explorer (RXTE). We
reveal that the X-ray broad-band energy spectra during all spectral states can
be reproduced by a {physical} model, composed of a soft blackbody component,
{two Comptonized components (both due to the presence of that TL that
up-scatters 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 kT_e changes from 3
to 21 keV along Z-track. We interpret the detected quasi-stability of the
indices of Comptonized components near a value of 2. Furthermore, this index
stability now found for the Comptonized spectral components of Z-source GX
340+0 is similar to that was previously established in the atoll sources
4U~1728-34, GX 3+1 and early 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 high mass accretion rate.
