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.
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