A composite elastic nonwoven web consisting essentially of:from about 50-99 percent, by weight, of a coherent matrix of meltblown fibers which consists of a polyether block amide copolymer having the formula of ##STR4## where n is a positive integer, PA represents a polyamide segment and PE represents a polyether segment; and from about 1-50 percent, by weight, of at least one type of other fibers