Multiphoton ionization rates have been calculated for He at the KrF laser w
avelength of 248 nm and for laser intensities up to 6 x 10(14) W cm(-2) usi
ng the R-matrix Floquet method. For intensities above that at which channel
closing takes place it is found that intermediate five-photon resonances w
ith bound states strongly influence the total rare, In particular, the reso
nance between the ground state and the 1s2p P-1(O) stare is found to occur
at a laser intensity of 5 x 10(14) W cm(-2). This resonance is investigated
at several neighbouring wavelengths and its prominent nature, which is dis
cussed in terms of a proposed nearby laser-induced degenerate stare, should
enable it to be observed experimentally.