MeV sputtering from CsI and organic samples induced by the polyatomic ions Cn+ (n = 1–12), Agn+ (n = 1–7), and Aun+ (n = 1–5) has been investigated. It is found that the desorption yield Yn increases more than linearly with increasing nonber n of projectile constituents. In case of the Cn+ induced desorption from a CsI sample it could be shown that the nonlinear increase of Yn reflects a linear increase of the energy density produced by the cluster projectile. This is a collective effect resulting from the simultaneous action of all n constituents of the polyatomic ion.