  In this paper detailed neutron scattering measurements of the magnetic
excitation spectrum of CuCrO$_2$ in the ordered state below $T_{\rm{N1}}=24.2$
K are presented. The spectra are analyzed using a model Hamiltonian which
includes intralayer-exchange up to the next-next-nearest neighbor and
interlayer-exchange. We obtain a definite parameter set and show that exchange
interaction terms beyond the next-nearest neighbor are important to describe
the inelastic excitation spectrum. The magnetic ground state structure
generated with our parameter set is in agreement with the structure proposed
for CuCrO$_2$ from the results of single crystal diffraction experiments
previously published. We argue that the role of the interlayer exchange is
crucial to understand the incommensurability of the magnetic structure as well
as the spin-charge coupling mechanism.
