Thin liquid sheets are present in a variety of systems and applications. Here, we are interested in double-layered sheets, which are common in the curtain coating process. In curtain coating, the liquid falls from a die forming a thin curtain before wetting the moving substrate. One of the most important process limits is the curtain breakup, which sets a lower limit for the coating liquid flow rate. Consequently, this flow rate lower limit defines the feasible minimum deposited film thickness. Experimental evidence have shown that using a two-layer curtain, with a viscoelastic thin layer, may delay the curtain breakup to lower flow ratios. The breakup of two-layer liquid sheets, composed of a Newtonian and a viscoelastic liquid, is studied by solving the differential equations that describe the evolution of the liquid sheet configuration until breakup. The effect of different parameters on the breakup time is determined. The results show the same behavior observed experimentally, thin viscoelastic liquid layer delays the breakup, stabilizing the liquid sheet.