Magnetization steps from Mn 2ϩ pairs in several single crystals of Zn 1Ϫx Mn x O (0.0056рxр0.030), and in one powder (xϭ0.029), were observed. They were used to determine the four largest exchange constants ͑largest J's͒, and the single-ion axial anisotropy parameter D. The largest two exchange constants, J 1 /k B ϭϪ18.2Ϯ0.5 K and J 1 Ј/k B ϭϪ24.3Ϯ0.5 K, were obtained from large peaks in the differential susceptibility, dM /dH, measured in pulsed magnetic fields H up to 500 kOe. These two largest J's are associated with the two inequivalent classes of nearest neighbors ͑NN's͒ in the wurtzite structure. The 29% difference between J 1 and J 1 Ј is substantially larger than 13% in Cd 1Ϫx Mn x S and 15% in Cd 1Ϫx Mn x Se. The pulsed-field data also indicate that, despite the direct contact between the samples and a superfluid-helium bath, substantial departures from thermal equilibrium occurred during the 7.4-ms pulse. The third-and fourth-largest J's were determined from the magnetization M at 20 mK, measured in dc magnetic fields H up to 90 kOe. Both field orientations Hʈc and Hʈ͓101 0͔ were studied. ͑The ͓101 0͔ direction is perpendicular to the c axis, ͓0001͔.͒ By definition, neighbors which are not NN's are distant neighbors ͑DN's͒. The largest DN exchange constant ͑third-largest overall͒ has the value J/k B ϭϪ0.543Ϯ0.005 K, and is associated with the DN at rϭc. Because this is not the closest DN, this result implies that the J's do not decrease monotonically with the distance r. The second-largest DN exchange constant ͑fourth-largest overall͒ has the value J/k B ϷϪ0.080 K. It is associated with one of the two classes of neighbors that have a coordination number z n ϭ12, but the evidence is insufficient for a definite unique choice. The dependence of M on the direction of H gives D/k B ϭϪ0.039 Ϯ0.008 K, in fair agreement with Ϫ0.031 K from earlier electron paramagnetic resonance work.