In this thesis topics of optimal experimental design for linear and non-linear mixed models are considered. This is motivated by the field of application of population pharmacokinetics in drug development. Thus, examples from this area will be used throughout this thesis for illustration purposes. First an introduction to the well-known topic of optimal experimental designs for the ordinary linear model is given. Then the linear and non-linear mixed models that are considered within this thesis are introduced. Focus is, on one hand, put on the so-called random coefficient regression model, which is a regression model with random parameters, and, on the other hand, on a more general mixed model, where additional factors that are not to be controlled by the investigator are included into the model. After this, a general definition of designs in mixed models is given. The designs are defined in two stages: The first stage are the elementary designs, which specify the settings for single individuals, while the second stage are population designs, by which the settings for the whole sample population are defined. On both levels we allow approximate designs. As designs are usually evaluated by using real-valued functions of the respective information matrices, we derive different representations of the information matrices for the introduced designs, which allow their calculation also for approximate designs. Two extreme cases of classes of population designs are considered. These are, on one hand, the single-group designs, where all individuals are observed under the same experimental settings and, on the other hand, general population designs, where different settings are allowed for different individuals. We show that the design optimization can be restricted to the class of single group designs if the mean number of observations per individual is prespecified and criteria are considered that are only based on the population parameter vector and not on the variance parameters. The larger class of general population designs then does not contain better designs. This result is extended to the considered general mixed models. In this case, however, one elementary design for each distinct value of the uncontrolled factor is necessary. Besides this, equivalence theorems, similar to the ones known for the ordinary linear model, are derived for various situations. They allow to check the optimality of given designs. The thesis closes with a discussion, in which also practical aspects of experimental designs for population pharmacokinetic studies are addressed.