Meltblown nonwoven compositions and processes for forming them are described herein. In one or more embodiments, the invention is directed to meltblown nonwoven fabrics having at least one elastic layer, wherein the elastic layer comprises a propylene-based polymer having an MFR greater than about 25 g/10 min. Additionally, the propylene-based polymer comprises from about 5 to about 25 wt % of one or more C2 and/or C4-C12 α-olefins and has a triad tacticity greater than about 90% and a heat of fusion less than about 75 J/g. The present invention is also directed to processes for forming meltblown nonwoven fabrics comprising forming a molten propylene-based polymer having an MFR of at least about 25 g/10 min, forming fibers comprising the propylene-based polymer, and forming an elastic nonwoven layer from the fibers.