Within the population of voiceband telephone channels, few channel characteristics are as pervasive in their impairment of high-speed data communication as nonlinear distortion, which cannot be removed or equalized in the receiver as easily as can linear distortion. The purpose of this paper is to report on an investigation of a QAM receiver incorporating adaptive equalization of nonlinearities as well as adaptive decision feedback equalization and data-aided carrier recovery for mitigation of linear distortion and phase jitter, respectively. Nonlinearities are equalized by adding to the received in-phase and quadrature signals a weighted sum of nonlinear functionals of the received signal and of modulated previous receiver decisions. The choice of nonlinear terms in the sum is based on a channel model incorporating quadratic and cubic nonlinearities as well as linear dispersive elements. The adjustment of the weighting, or tap, coefficients for the various terms is based on a gradient algorithm, as is the adjustment of the linear tap coefficients and the carrier phase reference. The feasibility of nonlinearity equalization on real voiceband channels was confirmed in a test in which recorded 9600-bps QAM signals, received from a worse-than-average set of 17 voiceband telephone channels, were processed by a computer-simulated version of the proposed receiver (termed the NL receiver). The observed error rates for all channels were lower, in some cases by several orders of magnitude, than those achieved by computer-simulated versions of the linear receiver and of a decision feedback equalization receiver (termed the DFE receiver).