  The coherent optical response from 140~nm and 65~nm thick ZnO epitaxial
layers is studied using transient four-wave-mixing spectroscopy with picosecond
temporal resolution. Resonant excitation of neutral donor-bound excitons
results in two-pulse and three-pulse photon echoes. For the donor-bound A
exciton (D$^0$X$_\text{A}$) at temperature of 1.8~K we evaluate optical
coherence times $T_2=33-50$~ps corresponding to homogeneous linewidths of
$13-19~\mu$eV, about two orders of magnitude smaller as compared with the
inhomogeneous broadening of the optical transitions. The coherent dynamics is
determined mainly by the population decay with time $T_1=30-40$~ps, while pure
dephasing is negligible in the studied high quality samples even for strong
optical excitation. Temperature increase leads to a significant shortening of
$T_2$ due to interaction with acoustic phonons. In contrast, the loss of
coherence of the donor-bound B exciton (D$^0$X$_\text{B}$) is significantly
faster ($T_2=3.6$~ps) and governed by pure dephasing processes.
