  Various aspects of the application of Effective Field Theory (EFT) to the
Nucleon-Nucleon (NN) interaction are considered. We look for contributions
beyond One Pion Exchange which are predicted by Chiral Symmetry.
  Using the formalism of the Wilson Renormalisation Group (RG) we review power
counting in a simplified EFT containing only nucleons. For weak scattering at
low energy, we find a natural expansion of the scattering matrix around the
unique trivial fixed point of the RG. For strong scattering at low energy, the
calculation can be organised in a useful and systematic way by expanding the
potential around a non-trivial fixed point corresponding to a bound state of
two nucleons at threshold. The resulting expansion of the inverse of the
scattering matrix reproduces the effective range expansion order by order.
  The extension of this EFT to include pions in a manner consistent with chiral
symmetry is discussed. By considering a modified effective range expansion, we
find that the small momentum expansion in S-wave scattering converges slowly,
if at all. The NN potential is written down to third order in small momenta.
With a cut-off in coordinate space, we calculate phase shifts in peripheral
partial waves for which the EFT predictions are parameter-free, and for which
we may use the expansion around the trivial fixed point. We find several
partial waves in which the effects of two-pion exchange can be isolated, but no
strong evidence is found for the convergence of the small momentum expansion at
this order.
