Dielectric relaxation times are often interpreted in terms of the reorientation of dipolar species or aggregates. The relevant time correlation function contains, however, cross terms between dipole moments of different particles. In the static case, these cross terms are accounted for by the Kirkwood factor g(K). Theories and molecular dynamics simulations suggest that such cross correlations may also affect the time-dependent properties, as reflected in the dielectric spectra. We present an experimental method for detecting effects of such cross correlations in dielectric spectra by a comparative analysis of dielectric and magnetic relaxation data. We demonstrate that such collective contributions can substantially affect dielectric relaxation. Experiments for n-pentanol (g(K) = 3.06 at 298 K) and 2,2-dimethyl-3-ethyl-pentane-3-ol (g(K) = 0.59) and their solutions in carbon tetrachloride show that in systems with g(K). 1, the cross correlations slow down dielectric relaxation. In systems with g(K) < 1, dielectric relaxation is enhanced. The results conform to theoretical predictions by Madden and Kivelson [Adv. Chem. Phys. 56, 467 (1984)] and to results of molecular dynamics simulations. The relaxation enhancement by cross terms in the case of g(K) < 1 is difficult to rationalize by conventional models of dielectric relaxation. (C) 2004 American Institute of Physics.