(57) @ A process for producing a composite monofilament of sheath-and-core type having heat-adhesive properties, super- iorstrengths, no curl and no peeling of the composite components is provided, which process comprises subjecting a low melting polyolefin selected from high density polyethylene, linear chain, low density polyethylene, polypropylene (PP) of m.p. 135°C or lower, or mixture thereof, and a high melting PP of m.p. 150°C or higher, to a sheath-and-core type composite spinning using the former resin as the sheath component and the latter resin as the core component, into a composite monofilament, the melt flow index ratio of the former component to the latter being 1.5 - 7, and the composite ratio being 30: 70 to 60 : 40; and stretching the composite filament to 6 - 9 times.