The recursive least-squares estimation technique is extended for application to systems with small but unknown dead-time delays. In this paper, the problem is studied with particular reference to the diesel engine used as a prime-mover for which the dead-time leads to a significant variation of dynamic performance. In practice, least-squares estimators are found to have slow convergence and large output errors, when applied to systems with time-delays. It is shown that by a suitable constrained algorithm, convergence can be quickened and output error can be kept within acceptable limits. Low order system models with changing dead-time are, in general, characterised by modelling errors that are to an extent correlated with the input control signal to the plant. Despite this fact, the development approach yields very small prediction errors, even when large, deterministic disturbances are present. This suggests its possible use in conjunction with adaptive controllers of various types.