Detection and classification of extracellularly recorded spikes, which is often referred to as "spike sorting", is one of major problems in neural signal processing. In spike sorting, independent detection and accurate classification of overlapped spikes have been difficult, and the traditional approach using thresholding, clustering and template matching often results in invalid estimation under many overlaps. To solve this issue, we have developed the spike sorting system that can process arbitrarily overlapped spikes. Our spike sorting system is based on approximated sequential Bayesian inference and Expectation-Maximization algorithm with probabilistic models of spike generation and extracellular voltage recording and does not depend on the amplitude threshold and clustering methods. The probabilistic model that describes all possibilities of spike trains including overlaps enables the system to detect overlapped spikes accurately, and approximation of low probabilities to zero in the inference reduces computational cost enough to process in standard laptop computers. There are two algorithms, the first is for fast processing under given spike templates and the second is for the simultaneous estimation of spike templates and spike timings. Both offline and online applications are realized by the complementary usage of two algorithms. The evaluation using simulated signals revealed that the algorithms showed high estimation accuracy even in extremely dense spike trains in which traditional spike sorting methods cannot extract valid spike trains and spike templates, which implied robustness of the algorithms to spike overlaps. Furthermore, as the result of application to various real neural signals, it was showed that the system could decompose complexly overlapped spikes that could not be detected appropriately by traditional approach. This work was supported by Grant-in-Aid for JSPS Fellows.