In this paper we develop two sequential or "on-line" estimation schemes in the time domain for dynamic shock-error models which are special cases of errors-in-variables models. Our approach utilizes a state-space representation of the model, Kalman filtering techniques, and on-line algorithms. The first on-line algorithm is based on the expectation-maximization algorithm and uses a recursive Gauss-Newton scheme to maximize the Kullback Leibler information measure. The second on-line algorithm we propose is a gradient-based scheme and uses stochastic approximations to maximize the log likelihood. In comparison to the off-line Maximum Likelihood estimation scheme used in [1], our on-line algorithms have significantly reduced computational costs and negligible memory requirements. Simulations illustrate the satisfactory performance of the algorithms in estimating errors-in-variables systems with parameters that vary slowly with time or undergo infrequent jump changes.