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We propose a method for online Thai handwritten character recognition using HMMs and SVMs with score-space kernels. Score-space kernels are generalized Fisher kernels based on underlying generative models, such as Gaussian mixture models (GMMs), which are output distributions of each state in HMMs. Our system combines the advantages of both generative and discriminative classifiers. In the first phase, HMMs are used for multi-classification, then SVMs are applied to resolve any uncertainty remaining after the first-pass HMM-based recognizer, but they are not applied for all classes because the results of some classes are worse. We consider the HMM confusion matrix to find the confused candidates in each class. If there is one candidate, it means there is no confusion in this class, and HMMs alone are sufficient to classify. SVMs are applied if there is more than one candidate. If there are more than two, the multi-class method is applied. On account of the basic score-spaces, likelihood and likelihood ratio score-spaces are not symmetrical. In the case of likelihood score-space, the parameters refer to only one generative model from two class models. In the case of likelihood ratio score-space, the parameters refer to both of them, but in different positions; thus one observation sequence can map to two score-vectors. We propose a new symmetric score-space, called symmetric likelihood ratio score-space. In this way, one observation sequence is mapped to only one score-vector. Experimental results show the average recognition rate improved from 89.9%, using baseline HMM, to 92.5%, using our proposed method.