Complex permittivities of in vitro diseased and undiseased human female breast tissues have been measured at 3.2 GHz using a resonant cavity technique. Ranges of dielectric properties and water contents of these tissues are presented. Experimental data are compared with models predicted from mixture equations. Measured permittivity data lie within limits set by two-phase mixture theory, but some conductivity data are in excess of those expected for a mixture of saline and protein. At any particular microwave frequency in all tissue of a given type, the relationship between permittivity and conductivity may be parametrized using the Debye relaxation equations. For each breast tissue type a characteristic relaxation frequency was calculated and found to be lower than that of physiological saline at the same temperature. It is concluded that the dielectric relaxation of tissue water is not the only dispersive process occurring at this frequency: dielectric relaxation of bound water and the tail end of a beta-dispersion may also contribute to the dielectric properties. The similarity of the dielectric properties of benign and malignant breast tumours measured in this work suggest that in vivo dielectric imaging methods will not be capable of distinguishing them.