Stretchable film laminates including a layer of elastomeric openwork, such as a plurality of elastic strands or an elastomeric mesh structure. The stretchable film laminates may include a film layer bonded to the layer of elastomeric openwork, with the film layer having cross-directional stretch and the laminate having a multi-phase stretchability profile. The stretchable film laminates may be made by extruding a film from a die, stretching the film, forming and stretching a layer of elastomeric openwork, conveying the stretched elastomeric openwork onto the film while the film is stretched, and passing the film and the elastomeric openwork through a nip. The invention also includes a machine capable of producing machine-direction, cross-direction, and biaxial stretch materials. The machine includes at least one extruder, at least one filament die and at least one film die both attached to the extruder(s), and at least one nip downstream of the extruder(s).