The recurrent algorithm for pursuing a time-varying ("drifting") quantile is suggested. The common nonasymptotic upper bound of the algorithm quality is established, which is then used in a few examples of the conditions for the quantile drift function. Estimates of the degree (rate) of convergence of the algorithm for the considered examples are obtained. Original Russian Text © E.N. Belitser, P. Serra, 2013, published in Avtomatika i Telemekhanika, 2013, No. 4, pp. 91–109.