A mathematical model is described which generates a pulse waveform identical to that of a single-integrator delta modulator, provided that the input signals to the latter do not cause slope overloading. The model uses analogue techniques of angle modulation and sampling to generate time- and amplitude-quantised signals, thus readily lending itself to exact analysis. The delta-modulation process is treated in a general manner that is equally applicable to delta-entry and sigma-entry systems. By this means, a central delta modem is defined which includes both pulse modulation and local decoding (prior to final filtering) of the pulse waveform. The model formulation is such that it is equivalent to the delta modem. The equivalence of the delta modem and model is proved analytically. It has also been verified by simulation on a digital computer and demonstrated experimentally. The model can be extended to simulate a double-integration network, provided that the necessary prediction is included. The model can also be extended to represent pulse-code modulation, because a linearly quantised p. c. m. siganal can be obtained by suitable sampling of the output of a delts modulator.