In the design of identification algorithms, the dead-time is usually modelled by some form of a polynomial function that adequately approximates the dead-time behaviour over relevant frequency bands.The application of all-zero models for approximation of plant dead-times is discussed. Gain-error criterion is established for a general model, whereas phase-error criterion is presented for first-order approximations. It is shown that if a plant transfer function has lowpass features, it is possible to determine a satisfactory all-zero model for the delay.The modelling technique is applied in a recursive least-squares based identification algorithm. This is used to obtain a delay-model predictor. Adaptive controllers, of thek-incremental predictive type, are set up using the identification results.