This paper explores the modelling of inter-frame dependence as a means of improving the performance of HMMs. More specifically, a model based on the IFD- HMM (Ming & Smith, 1996) that assumes a dependency upon both succeeding and preceeding frames is proposed. The means by which a dependency upon succeeding frames might be integrated into a HMM framework are explored, and a mathematical outline of the proposed extension given. The results of various tests aimed towards exploring the consequences of introducing succeeding frame dependencies are included. It was found that a dependency upon succeeding frames enabled dynamic spectral information, not found in the preceeding frames, to be usefully employed; resulting in a significant increase in the recognition accuracy. Additionally, it was shown that modelling of the dynamic spectral information (using time-lag sequences) was at least as important as improved modelling of the instantaneous spectra (using multiple mixtures).