The invention relates to an apparatus for melt spinning a plurality of composite yarns, which each consist of a plurality of extruded filament bundles. To this end, the apparatus comprises a plurality of spinnerets and a cooling device associated to at least one of the spinnerets for cooling the filament bundles, a combining means for bundling the filament bundles forming the composite yarns, anda withdrawal means for withdrawing the filament bundles. To obtain the most identical spacing possible between yarns in the production of the composite yarns, the invention provides for distributing the spinnerets over a plurality of parallel spin groups, with each spin group comprising spinnerets arranged side by side in rows. Each spinneret of a first spin group forms with at least one spinneret of a second spin group arranged in a common spinning plane, a spinning position for producing one of the composite yarns.