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Multiple acoustic models are often combined in statistical parametric speech synthesis. Both linear and non-linear functions of an observation sequence are used as features to be modeled. This paper shows that this combination of multiple acoustic models can be expressed as a product of experts (PoE); the likelihoods from the models are scaled, multiplied together, and then normalized. Normally these models are individually trained and only combined at the synthesis stage. This paper discusses a more consistent PoE framework where the models are jointly trained. A training algorithm for PoEs based on linear feature functions and Gaussian experts is derived by generalizing the training algorithm for trajectory HMMs. However for non-linear feature functions or non-Gaussian experts this is not possible, so a scheme based on contrastive divergence learning is described. Experimental results show that the PoE framework provides both a mathematically elegant way to train multiple acoustic models jointly and significant improvements in the quality of the synthesized speech.