  We consider nucleon-nucleon ($NN$) interactions from Chiral Effective Field
Theory applying the $N/D$ method. The dynamical input is given by the
discontinuity of the $NN$ partial-wave amplitudes across the left-hand cut
(LHC) calculated in Chiral Perturbation Theory (ChPT) by including one-pion
exchange (OPE), once-iterated OPE and leading irreducible two-pion exchange
(TPE). We discuss both uncoupled and coupled partial-waves. We show
algebraically that the resulting integral equation has a unique solution when
the input is taken only from OPE because it is of the Fredholm type with a
squared integrable kernel and an inhomogeneous term. Phase shifts and mixing
angles are typically rather well reproduced, and a clear improvement of the
results obtained previously with only OPE is manifest. We also show that the
contributions to the discontinuity across the LHC are amenable to a chiral
expansion. Our method also establishes correlations between the $S$-wave
effective ranges and scattering lengths based on unitarity, analyticity and
chiral symmetry.
