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Visualization and tracking of single fluorescent molecules is a recent development in optical microscopy holding great promise for the study of cell biological processes. However, the detection and characterization of single molecules in three-dimensionally (3D) extended systems such as living cells has yet to be accomplished. By carefully choosing the hardware components of the microscope and a detailed theoretical description of the imaging process, the imaging conditions could be optimized for single molecule tracking experiments inside the cell nucleus. We developed a two-color widefield fluorescence microscope equipped with an Ar-laser and a He-Ne-laser and two CCD cameras. By programming the hardware of the CCDs we achieve a maximum frame repetition rate of 125Hz. In the first step single protein molecules of the green fluorescent protein (GFP) were detected at room-temperature in 3D-solutions with a time resolution of up to 13ms. The 2D localization precision was determined to be ~25nm. From the trajectories, the diffusion coefficients of single GFP molecules were derived and found to agree well with theoretical expectations. Using the recombinant E. coli ß-galactosidase protein P4K, single molecules could be tracked in the nuclei of 3T3-cells at a spatial accuracy of ~30nm and a time resolution of 18ms. These results suggest that proteins can move inside the nucleus over extended distances by diffusion. However, intranuclear protein diffusion is severely restricted, most likely by multiple association-dissociation events and/or impermeable obstacles. In a further step we examined the intranuclear dynamics of the splicing-factor U1-snRNP on a single molecule level. From these results we derived a model for the dynamics of U1-snRNPs. This model substantiates the view that nuclear speckles are not rigid structures but highly dynamic domains characterized by a rapid turnover of U1-snRNPs and other splicing factors.