We present the results of R-matrix Floquet calculations for generalized two- and three-photon ionization cross sections of neonand argon in the XUV region. Photoionization is strongly enhanced by singly- anddoubly-excited resonances. We show that interference effects between different Rydbergstates can strongly modify the photoionization cross sections. The observation ofthree- and four-photon resonances in the two- and three-photon spectra, respectively,demonstrates the influence from higher-order processes. The cross sections may be usedto estimate the intensity attained by harmonic radiation in the XUV region.