  Within the one-loop approximation of baryon chiral perturbation theory we
calculate all one-pion and two-pion exchange contributions to the
nucleon-nucleon interaction. In fact we construct the elastic NN-scattering
amplitude up to and including third order in small momenta. The phase shifts
with orbital angular momentum $L\geq2 $ and the mixing angles with $J\geq2$ are
given parameterfree and thus allow for a detailed test of chiral symmetry in
the two-nucleon system. We find that for the D-waves the $2\pi$-exchange
corrections are too large as compared with empirical phase shifts, signaling
the increasing importance of shorter range effects in lower partial waves. For
higher partial waves, especially for G-waves, the model independent
$2\pi$-exchange corrections bring the chiral prediction close to empirical NN
phase shifts. We propose to use the chiral NN phase shifts with $L\geq 3$ as
input in a future phase shift analysis. Furthermore, we compute the irreducible
two-pion exchange NN-potentials in coordinate space. They turn out to be of
van-der-Waals type, with exponential screening of two-pion mass range.
