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This paper adapts the classical list-mode OSEM and the globally convergent list-mode COSEM methods to the special case of singleton subsets. The image estimate is incrementally updated for each coincidence event measured by the PET scanner. Events are used as soon as possible to improve the current image estimate, and, therefore, the convergence speed toward the maximum-likelihood solution is accelerated. An alternative online formulation of the list-mode COSEM algorithm is proposed first. This method saves memory resources by re-computing previous incremental image contributions while processing a new pass over the complete dataset. This online expectation-maximization principle is applied to the list-mode OSEM method, as well. Image reconstructions have been performed from a simulated dataset for the NCAT torso phantom and from a clinical dataset. Results of the classical and event-by-event list-mode algorithms are discussed in a systematic and quantitative way.