This paper presents a new application of the well known stochastic approximation scheme to the problem of joint estimation of the time delay (dead time) and process parameters, as it occurs in the context of plant identification. In this new application, the unknown delay κ is included along with the other ARMAX parameters in a conventional direct LS recursive estimation scheme. The introduction of the unknown delay requires the evaluation of additional error sensitivity functions. This is done originally by approximating the operator d/dκ with —(I — z-1), where z-1is the shift operator. Three versions of the algorithm are presented, with increasing levels of complexity. The operation of the simplest version is illustrated by simulations