  We develop an approach describing nonlinear-optical processes in the
strong-field domain characterized by the nonperturbative field-with-matter
interaction. The polarization of an isolated atom in the external field
calculated via the numerical solution of the time-dependent Schr\"odinger
equation agrees with our analytical findings. For the practically important
case of one strong laser field and several weaker fields we derive and
analytically solve propagation equations describing high-order (HO)
wave-mixing, HO parametric amplification and HO stimulated scattering. These
processes provide a way of efficient coherent XUV generation. Some properties
of HO processes are new in nonlinear optics: essentially complex values of the
coefficients in the propagation equations, the super-exponential (hyperbolic)
growing solutions, etc. Finally, we suggest conditions for the practical
realization of these processes and discuss published numerical and experimental
results where such processes could have been observed.
