The coherent optical response from 140 nm and 65 nm thick ZnO epitaxial layers is studied using 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 (D0XA) at temperature of 1.8 K we evaluate optical coherence times T2=33-50 ps corresponding to homogeneous line widths of 13-19μeV, 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 T1=30-40 ps, while pure dephasing is negligible. Temperature increase leads to a significant shortening of T2 due to interaction with acoustic phonons. In contrast, the loss of coherence of the donor-bound B exciton (D0XB) is significantly faster (T2=3.6ps) and governed by pure dephasing processes.