This thesis is primarily concerned with the development of adaptive algorithms for equaliser coefficient computation within the highly time variant radio communications environment. More specifically the problem of equaliser coefficient computation within the pan European digital mobile radio system is considered. The work encompasses both equaliser and channel estimator adaptive algorithms and techniques for the automatic synthesis of linear transversal equalisers (LTE), decision feedback equalisers (DFE) and adaptive maximum likelihood sequence estimators (MLSE) are developed. Within the thesis it is shown that equaliser performance can be significantly improved by adaptively updating the equaliser throughout unknown data transmission. Initially the performance of conventional techniques, such as gradient search (GS) and least squares (LS) algorithms, when employed in this respect is investigated. Although each is shown to yield performance improvement over the system in which no adaptive update is employed, it is shown that under highly time variant conditions the performance of the conventional algorithms is subject to several limitations. This conclusion provides the motivation for the development of a number of alternative adaptive algorithms which offer performance advantage under highly time variant conditions. Two classes of algorithm are proposed. Within each a priori knowledge of the time variant characteristics of the channel is used in order to partially cancel estimation error due to the channel time variation. Within the first this is achieved by augmenting the update equation of each of the conventional algorithms by inclusion of an additional parameter set representing an estimate of the rate of change (ROC) of the channel coefficients. The algorithms are thereby able to form a prediction of the instantaneous channel variation and, therefore, to compensate for the channel non-stationarity. In the second class of algorithm a predetermined model of channel time variability is incorporated directly into the algorithm structure.