  We determine the UHE neutrino-nucleon cross-sections analytically both for
charged and neutral current in the leading order by using the solutions of
non-singlet DGLAP equation as well as singlet DGLAP equation respectively. Next
we determine the cross-sections for both charged and neutral current at one
loop level by carring out numerical integration of the double differential
cross-section. For analytical solution, we take the standard MRST 2004 f4 LO
parton distributions at $Q_0^2=1$ \,GeV$^2$ as input and for numerical solution
(exact), we consider the GRV 94 parton distributions. Our analytical as well as
numerically determined results are compared with the NLO results of various
authors. We find our numerically determined result in sufficient agreement with
the results obtained by those authors. On the other hand, our analytical result
matches better with other results at lower end of the energy spectrum of the
UHE neutrino rather than the higher end.
