  We provide a detailed quantitative study of the possible role of a small
admixture of harmonics on resonant two-photon ionization. The motivation comes
from the occasional presence of 2nd and 3rd harmonics in FEL radiation. We
obtain the dependence of ionic yields on the intensity of the fundamental, the
percentage of 2nd harmonic and the detuning of the fundamental from resonance.
Having examined the cases of one and two intermediate resonances, we arrive at
results of general validity and global behavior, showing that even a small
amount of harmonic may seem deceptively innocuous.
