In this paper we apply the Full Combination (FC) multi-band approach, which has originally been introduced in the framework of posterior-based HMM/ANN (Hidden Markov Model/Artificial Neural Network) hybrid systems, to systems in which the ANN (or Multilayer Perceptron (MLP)) is itself replaced by a Multi Gaussian HMM (MGM). Both systems represent the most widely used statistical models for robust ASR (automatic speech recognition). It is shown how the FC formula for the likelihood--based MGMs can easily be derived from the posterior-based approach by simply applying Bayes' Rule. The experiments show that the Full Combination multi-band system with MGM experts performs better, in all noise conditions tested, than the simple sum and product rules which are normally used. As compared to the baseline full-band system, the FC system shows increased robustness mainly on band-limited noise. The goal of this article is not a performance comparison between Multilayer Perceptrons and Multi Gaussian Models but between the theory of the two approaches, posterior-based vs. likelihood-based FC approach, so results are only given for the MGMs.