The estimation of Hidden Markov Models has attracted a lot of attention recently, see results of Legland and Mevel (2000) and Leroux (1992). The purpose of this paper is to give a view for the analysis of the maximum-likelihood estimation of HMM-s. General consistency results are compared to the new approach. The new approach is potentially useful for deriving strong approximation results, which are in turn applicable to analyze adaptive predictors.