### Summary

Dynamic exponential family regression provides a framework for nonlinear regression analysis with time dependent parameters*β*_{0},*β*_{1}, …,*β*_{t}, …, dim*β*_{t}=*p*. In addition to the familiar conditionally Gaussian model, it covers e.g. models for categorical or counted responses. Parameters can be estimated by extended Kalman filtering and smoothing. In this paper, further algorithms are presented. They are derived from posterior mode estimation of the whole parameter vector (*β*′_{0}, …,*β*′_{t}) by Gauss-Newton resp. Fisher scoring iterations. Factorizing the information matrix into block-bidiagonal matrices, algorithms can be given in a forward-backward recursive form where only inverses of “small”*p×p*-matrices occur. Approximate error covariance matrices are obtained by an inversion formula for the information matrix, which is explicit up to*p×p*-matrices.