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In this paper, a moving algorithm for on-line identification of continuous-time systems is developed. With the proposed algorithm, the observed input–output data can be directly used to estimate the system parameters without any numerical pre-processing, and by means of a recursive formula the estimates can be updated step by step without repeatedly computing the matrix inversion. In this way, the use of both computer memory and computing time can be reduced. Besides, the computations are simple and straightforward. From the moving identification algorithm, a linear moving model can be obtained to represent the control systems. The on-line optimal control algorithm is also developed via the linear moving model. A slider-crank motion control system is used to illustrate that the proposed on-line identification and optimal control algorithms can give satisfactory results. [Copyright &y& Elsevier]