The authors propose a bandwidthefficient, asynchronous multiple-access technique with superior probability of error performance. The technique, called waveform division mutipleaccess (WDMA), assigns distinguishable baseband waveforms to the transmitters, and transmissions are asynchronous and occupy the entire available bandwidth. In contrast to direct sequence spread spectrum multiple-access (DS/SSMA), each waveform is continuous over the entire signalling interval. The waveforms are selected to achieve a prescribed multiple-access capability and spectral efficiency. The authors postulate a correlation receiver and select the correlating waveform to minimise a worst case average error probability for each receiver, given the transmit waveforms. The requirements of the waveforms are formulated in the context of constrained optimisation. Plots are presented of typical waveforms, spectra, autocorrelation and partial cross-correlation functions. Also presented are error probability curves for noncoherent differential phase shift keying (DPSK) operating in a Gaussian environment. These results indicate that WDMA is a viable alternative to DS/SSMA in applications where bandwidth is scarce and strict security is of no concern. Potential applications are transmission of public safety (police, fire, medical etc.), utility and distress informations.