  The effective chiral theory of the in-medium NN interactions is considered.
  The shallow bound states, which complicate the effective field theory
analysis in vacuum do not exist in matter. We show that the next-to-leading
order terms in the chiral expansion of the effective Lagrangian can be
interpreted as corrections so that the expansion is systematic. The Low Energy
Effective Constants of this Lagrangian are found to satisfy the concept of
naturalness. The potential energy per particle is calculated. The problems and
challenges in constructing the chiral theory of nuclear matter are outlined.
