A specific mechanism for the intracellular translocation of nonvesicle-associated proteins is proposed. This movement machinery is based on the assumption that the cytoskeleton represents an interconnected network of filamentous macromolecules, which extends over the entire cytoplasm. Diffusion along the filaments provides an efficient way for movement and with this, for signal transduction, between various intracellular compartments. We calculate the First Passage Time (FPT), the average time it takes a signaling molecule, diffusing along the cytoskeleton, to arrive from the cell surface to the nucleus for the first time. We compare our results with the FPT of free diffusion and of diffusion in the permeating cytoplasm. The latter is hindered by intracellular organelles and the cytoskeleton itself. We find that for filament concentrations even below physiological values, the FPT along cytoskeletal filaments converges to that for free diffusion. When filaments are considered as obstacles, the FPT grows steadily with filament concentration. At realistic filament concentrations the FPT is insensitive to local modifications in the cytoskeletal network, including bundle formation. We conclude that diffusion along cytoskeletal tracks is a reliable alternative to other established ways of intracellular trafficking and signaling, and therefore provides an additional level of cell function regulation.