Non-viral gene transfer systems have evolved over the last decade into widely-used vectors for delivery of exogenous DNA to eukaryotic cells. Many studies in the field report on transfection efficiencies as a function of vector composition and, to a lesser extent, on single-molecule experiments of vector transport processes. However, work on time-resolved single-cell experiments of eukaryotic gene transfection has been circumstantial. This thesis is on image processing of experimental time-lapse studies and computational modelling of the resulting protein expression time courses. Cells were transfected with GFP-encoding plasmids and single-cell timelapse movies were evaluated using image analysis. To this purpose, a cell tracking algorithm that identifies cell shapes, assigns cell tracks and resolves errors or reports cell events was developed. The algorithm treats the mapping of detected shapes to cell traces as a linear assignment problem using the weighted superposition of normalized cell properties as cost. Singularities in cost indicate either events in the cellular life cycle which are reported or image analysis events which are resolved. The software increased the yield of usable time series from high-throughput experiments by a factor of approximately two and eliminated the need for tedious and bias-prone manual movie evaluation. The fluorescence intensity time-series obtained from experiments on epithelial lung cells exhibited a sigmoidal onset behavior that saturated to a steady-state. A phenomenological fit to these yielded the maximum expression level, the expression rate and the onset time. The distribution of steady state expression levels showed a broad Poisson-like shape which is indicative of an underlying stochastic process with a low success probability. This was modeled mathematically as a two-step stochastic process in collaboration with J.-T. Kuhr from the group of Prof. Frey. The first, low-probability step considered was the delivery of plasmid complexes into the nucleus and the second was the release and activation of a small number of plasmids from this complex. This conceptually simple model consistently explained the observed fraction of transfected cells and the expression level distribution. The mean number of transcribed plasmids per complex could be determined from the model, which in our experiments was approximately 3.0. The model also correctly predicted the color distribution in a co-transfection experiment with yellow and cyan fluorescing proteins. An alternative implementation of the model was developed using the Pi-calculus approach which allows the use of a non-exponential distribution and a potentially unbounded number of species. Simulation of the model yielded a detailed, bi-variate distribution of co-transfection results in terms of expressed plasmids and color ratios. To determine the factors that influence the delivery probability and the impact of timing on the transfection efficiency, a stochastic state model of the gene transfer pathway was created. This model used transition rates from literature and from single-particle experiments to accurately reproduce the onset time distribution. The model correctly predicted the shift in onset times and total efficiency induced by magnetofection compared to normal transfection. Further simulations elucidated possible strategies to improve the gene delivery process in terms of speed and efficiency. A drawback of the linear stochastic model described above was that the shapes of the individual time-traces produced by the model did not match the expression speed of the experimental curves. For this reason, the role of poly-A in mRNA degradation was investigated and a more detailed expression pathway was introduced in the model, that lead to an improved approximation to the experimental data.