We theoretically study nonlinear optics of excitons under intense THz irrad
iation. In particular, the linear near-infrared absorption and resonantly e
nhanced nonlinear sideband generation are described. We predict a rich stru
cture in the spectra which an be interpreted in terms of the quasienergy sp
ectrum of the exciton, via a remarkably transparent expression for the susc
eptibility, and show that the effects of strongly avoided quasienergy cross
ings manifest themselves directly, both in the absorption and transmitted s
idebands.