  We study mechanisms of multi-wavelength emissions (X-ray, GeV and TeV
gamma-rays) from the gamma-ray binary LS~5039. This paper is composed of two
parts. In the first part, we report on results of observational analysis using
four year data of \fermi\ Large Area Telescope. Due to the improvement of
instrumental response function and increase of the statistics, the
observational uncertainties of the spectrum in $\sim$100-300 MeV bands and
$>10$GeV bands are significantly improved. The present data analysis suggests
that the 0.1-100GeV emissions from LS~5039 contain three different components;
(i) the first component contributes to $<$1GeV emissions around superior
conjunction, (ii) the second component dominates in 1-10GeV energy bands and
(iii) the third component is compatible to lower energy tail of the TeV
emissions. In the second part, we develop an emission model to explain the
properties of the phase-resolved emissions in multi-wavelength observations.
Assuming that LS~5039 includes a pulsar, we argue that both emissions from
magnetospheric outer gap and inverse-Compton scattering process of
cold-relativistic pulsar wind contribute to the observed GeV emissions. We
assume that the pulsar is wrapped by two kinds of termination shock; Shock-I
due to the interaction between the pulsar wind and the stellar wind and
Shock-II due to the effect of the orbital motion. We propose that the X-rays
are produced by the synchrotron radiation at Shock-I region and the TeV
gamma-rays are produced by the inverse-Compton scattering process at Shock-II
region.
