  This work presents results of near-band gap magnetooptical studies on
(Zn,Mn)O epitaxial layers. We observe excitonic transitions in reflectivity and
photoluminescence, that shift towards higher energies when the Mn concentration
increases and split nonlinearly under the magnetic field. Excitonic shifts are
determined by the s,p-d exchange coupling to magnetic ions, by the
electron-hole s-p exchange, and the spin-orbit interactions. A quantitative
description of the magnetoreflectivity findings indicates that the free
excitons A and B are associated with the Gamma_7 and Gamma_9 valence bands,
respectively, the order reversed as compared to wurtzite GaN. Furthermore, our
results show that the magnitude of the giant exciton splittings, specific to
dilute magnetic semiconductors, is unusual: the magnetoreflectivity data is
described by an effective exchange energy N_0(beta-alpha)=+0.2+/-0.1 eV, what
points to small and positive N_0 beta. It is shown that both the increase of
the gap with x and the small positive value of the exchange energy N_0 beta
corroborate recent theory describing the exchange splitting of the valence band
in a non-perturbative way, suitable for the case of a strong p-d hybridization.
