System identification is the experimental modeling of a dynamic system whose parameters or underlying physical principles are not precisely known. In particular, measurement data in the form of input-output data sets can be used to estimate the parameters of a system model. The goal of this work is the application of numerical methods to realize the parametrization of a model such that it predicts the behaviour of a nonlinear dynamic system in an optimal way. The basis for the applied system identification algorithm is the minimization of the output error of the model. A goodness-of-fit criterion, the sum of squared vertical distances between the measurement data points and the simulated model output at these points in time, is to be minimized. As the model of a nonlinear dynamic system is described by nonlinear differential equations, a numerical solver for the solution of initial value problems in conjunction with a numerical optimization method for the solution of the ensuing nonlinear curve fitting problem are applied in the system identification procedure. This system identification algorithm is applied to solve a set of example problems: a free falling object that is subject to drag due to air, a nonlinear mass and spring system and a nonlinear dynamic friction model, the LuGre model. Different numerical solutions methods for initial value problems as well as different numerical optimization techniques are applied in the solution of these system identification problems based on synthetic measurement data. The influence of gaussian measurement noise on the identified parameters as well as the feasibility of utilizing multiple measurement data sets in order to eliminate this disturbance induced variation is investigated. Furthermore, the combination of measurement data sets corresponding to different excitation levels of the object of interest is explored - a procedure that is of special importance in the system identification of nonlinear systems in order to accurately identify all the model parameters.