We calculate the two-photon ionization of clusters for photon energies near
the surface plasmon resonance. The plasmon is described in a schematic jel
lium-RPA model assuming a separable residual interaction between electrons
determined so that the plasmon energy is reproduced. The ionization rate of
a double plasmon excitation is calculated perturbatively. In Na-93(+) clus
ters we find an ionization rate of the order of at most 0.05-0.10 fs(-1). T
his rate is used to determine the ionization probability in an external fie
ld in terms of the number of absorbed photon pairs and the duration of the
field. We discuss the dependence of the results on the choice of our empiri
cal separable force. The number of emitted electrons per pair of absorbed p
hotons is found to be small, in the range 10(-5) to 10(-3).