In this paper, we are interested in the analysis of regularized online algorithms associated with reproducing kernel Hilbert spaces. General conditions on the loss function and step sizes are given to ensure convergence. Explicit learning rates are also given for particular step sizes. Keywords and Phrases: Online learning algorithm, reproducing kernel Hilbert space, regularized sample error, general loss function AMS Subject Classification Numbers: 68T05, 62J02. † The author’s current address: Department of Computer Science, University College London, Gower Street, London, WC1E, England, UK. 1