The invention is directed to composite elastic nonwoven fabrics and processes for producing the same. The fabric includes a layer of inelastic continuous or staple fibers formed from a blend of polyethylene and polypropylene laminated to an elastic layer. Preferably, the composition of the fibers ranges between 5 to 50 percent by weight of polypropylene with the balance made up of polyethylene. The nonelastic fibers are capable of being highly elongated upon mechanical stretching without adversely impacting fiber tie down. Accordingly, a smooth, strong, coherent fabric is obtained, which is especially well suited for incorporation into disposable absorbent articles such as diapers, training pants, incontinence briefs and feminine hygiene products.