We report the generation of short-wavelength, high-order harmonics of
intense laser radiation from atom clusters. Clusters containing about
10(3) atoms are produced in a high-pressure gas jet. We show them to b
e a unique nonlinear medium. Compared with monomer gases they yield a
higher appearance intensity for a given harmonic order, stronger nonli
near dependence of harmonic signal on laser intensity, higher-order ha
rmonics, and reduced saturation of the harmonic signal at high laser i
ntensity.