  In this work the elastic scattering of two nucleons is calculated in chiral
effective field theory at next-to-leading order taking into account the coupled
N$\Delta$-, $\Delta$N- and $\Delta\Delta$-channels. To solve the coupled
channel scattering equation one needs as input the potentials for all
combinations of these initial and final states. Up to next-to leading order
these (transition) potentials arise from one-pion exchange, two-pion exchange
and contact interactions. For the two-pion exchange we give analytic
expressions for the spectral functions derived from all contributing one-loop
diagrams. The forms of the contact potentials at leading and next-to-leading
order are determined. We perform a fit of the low energy constants, that belong
to the $NN \rightarrow NN$ contact potential and contribute up to
next-to-leading order to $S$- and $P$-waves of NN scattering only. The
influence of the $\Delta$-isobar dynamics entering through the coupled channels
is studied in detail.
