Abstract: This invention concerns an elastic multilayer composite, comprising an elastic film layer sandwiched between a first elastic nonwoven layer and an optional second elastic nonwoven layer, and a process for making the same. The laminate is stabilized via bonding according to either: adhesive bonding between the film and nonwoven layer(s), direct extrusion lamination of the film to one or more nonwoven layer(s), or attachment of the film to one or more of the nonwoven layers at a plurality of points via thermopoint bonding. This invention also concerns a process for manufacturing an elastic multilayer composite, comprising: bonding under neutral tension or substantially neutral tension at least one elastic film layer to at least one elastic nonwoven layer.