In this paper, a theoretical framework is proposed for the introduction of the K-NN pdf estimator in an HMM-based speech recognition system. The estimation of the state output probabilities with the K-NN pdf estimator is shown to imply the introduction of a new parameter : the membership coefficient. To learn this coefficient with the Baum-Welch algorithm, a maximum likelihood (ML) reestimation formula is derived. This new formula is tested and compared with the formula we had introduced previously [1]. Then, the edition/condensation techniques are introduced in the context of Markov models in an attempt to improve the appropriateness of the reference data set to the K-NN HMM system. Two new algorithms are proposed for editing and condensing the reference set which present the advantage of being compatible with the K-NN rule.