Fiber optic filaments or ribbons are deflected by a system of sheaves to converge at final filament deflection sheaves which direct the filaments along the longitudinal direction of an assembly table. Successive sets of filament deflection sheaves stack the filaments into bundles which are separated by spacer elements which are likewise guided to the assembly table. Sensors at the final sheaves monitor the tensions in both the filaments and separators and a controller is used to adjust the tensions to compensate for frictional variations upstream of the final sheaves. The table is positioned at an angle to the machine axis so that the stacked filament bundles and separators can be wound about a rotating core by being drawn along the table by the rotating core for staggered and tangential application of the filaments about the core at the downstream end of the table. The apparatus and method can be used to produce optical fiber cables in which the fibers can be wound either within helical grooves formed within the core or about the cylindrical surface of a smooth core. Any number of filament units can be wound about the core and any number of filaments or ribbons can be stacked in one or more of the filament units or bundles. The apparatus and method of the invention are extremely versatile and can produce both simple and complex fiber optic cables including hundreds of fiber optic filaments, ribbons or strands in a simple and economical manner.