This work introduces two methods for adapting the observation process parameters of linear dynamic models (LDM) or other linear-Gaussian models. The first method uses the expectation-maximization (EM) algorithm to estimate transforms for location and covariance parameters, and the second uses a generalized EM (GEM) approach which reduces computation in making updates from $O(p^6)$ to $O(p^3)$, where $p$ is the feature dimension. We present the results of speaker adaptation on TIMIT phone classification and recognition experiments with relative error reductions of up to $6. Importantly, we find minimal differences in the results from EM and GEM. We therefore propose that the GEM approach be applied to adaptation of hidden Markov models which use non-diagonal covariances. We provide the necessary update equations.