This paper demonstrates that the non-linear system dynamics generating speech can be embedded in a low dimensional Euclidean space which resembles a manifold. Phoneme manifolds are extracted from the speech time series and compared using a radial basis function network to attempt speaker independent phoneme classification. The initial results are inconclusive but show promising results. Phoneme manifolds are also used for speech prediction resulting in a predictor which is able to achieve noise reduction equal to that of a nonlinear predictor but exhibits an improvement in the signal quality.