  We analyze the X-ray spectra of the atoll 4U~1705-44 when the source
undergoes the island-banana state transition. We use the Rossi X-ray Timing
Explorer (RXTE) and BeppoSAX observations for this analysis. We demonstrate
that the broad-band energy spectral distributions for all evolutinary states
can be fitted by a model, consisting two Comptonized components. One arises
from the seed photons coming from a neutron star (NS) atmosphere at a
temperature kT_{s1}<1.5 keV (herein Comptb) and a second resulting from the
seed photons of T_{s2}~1.1-1.3 keV coming from the disk (herein Comptb2). We
found that we needed to add a low-temperature blackbody and an iron-line
({Gaussian}) component to the model in order to obtain high-quality fits. The
data analysis using this model indicates that the power-law photon index
Gamma_{1} of our model is always about 2, independently of the spectral state.
Another parameter, Gamma_{2} demonstrates a two-phase behavior depending on the
spectral state. Gamma_{2} is quasi-constant at Gamma_{2}~ 2 when the electron
temperature kT^{(2)}_e<80 keV and Gamma_{2} is less than 2, in the range of
1.3<Gamma_{2}<2, when kT^{(2)}_e>80 keV. This phase is similar to that was
previously found in the Z-source Sco X-1. We interpret the decreasing index
phase using a model in which a super-Eddington radiation pressure from the
neutron star causes an expansion of the Compton cloud similar to that found
previously in Sco~X-1 during the Flaring branch.
