Disclosed herein are elastic laminate materials. The elastic laminate materials are laminates of extensible nonwoven fibrous webs and thermoplastic elastic materials. The laminate may be a two-layer composite material having a single nonwoven fibrous web bonded to one side of the thermoplastic elastic material, or it may be a three-layer composite having a nonwoven fibrous web bonded to each side of the thermoplastic elastic material. The extensible nonwoven fibrous webs may be carded staple fiber webs of staple fibers. The thermoplastic elastic material may be single-layer or multi-layer elastic films, or elastic fibrous layers. Where single- or multi-layer elastic films are used, the films may be breathable films. The elastic material, or some of the staple fibers, or both, may be selected such that the carded staple fiber webs are thermally compatible with the thermoplastic elastic material to facilitate laminate bonding. Processes for forming the elastic laminate material are also disclosed.