Mixed models are usually motivated by the desire to model accurately the marginal means of the responses while accounting for heterogeneity and correlation. Starting with the alternative goal of modeling the covariance accurately we show, using a special Cholesky decomposition and parameterization of a covariance matrix, that any dependence structure can be modeled using the more general dynamic conditionally linear mixed models. Here dynamic means using past responses as covariate and conditional linearity means that parameters entering the model linearly are random and nonlinear parameters are nonrandom. This setup is surprisingly similar to models obtained from the first-order linearization method applied to nonlinear mixed models, which offers several advantages. First, it allows for flexible and computationally tractable models which allow a wide array of covariance structures; these structures may depend on covariates and hence may differ across subjects. This class of models includes, for example, all standard linear mixed models, antedependence models, and Vonesh-Carter models. Second, it guarantees the fitted marginal covariance matrix of the data is positive definite. We develop methods for Bayesian inference and illustrate our results on data from a series of longitudinal depression studies.