  A simple scheme of population and detection of low-lying electronic
quadrupole modes in free small deformed metal clusters is proposed. The scheme
is analyzed in terms of the TDLDA (time-dependent local density approximation)
calculations. As test case, the deformed cluster $Na^+_{11}$ is considered.
Long-living quadrupole oscillations are generated via resonant two-photon
(two-dipole) excitation and then detected through the appearance of satellites
in the photoelectron spectra generated by a probe pulse. Femtosecond pump and
probe pulses with intensities $I = 2\cdot 10^{10} - 2\cdot 10^{11} W/cm^2$ and
pulse duration $T = 200 - 500$ fs are found to be optimal. The modes of
interest are dominated by a single electron-hole pair and so their energies,
being combined with the photoelectron data for hole states, allow to gather new
information about mean-field spectra of valence electrons in the HOMO-LUMO
region. Besides, the scheme allows to estimate the lifetime of electron-hole
pairs and hence the relaxation time of electronic energy into ionic heat.
