A spunbonded elastic nonwoven fabric comprises a web of bonded thermoplastic filaments of a thermoplastic elastomer. The spunbonded fabrics of the invention are prepared in a slot draw spunbonding process operated at a rate of less than about 2000 meters per minute. The elastic fabric is used in absorbent products, such as disposable diapers, adult incontinence pads, sanitary napkins and the like, and as coverstock for absorbent personal care products.