Multi-layer elastic air quenched blown film structures are disclosed which include: a first layer incorporating a propylene-based copolymer and optionally, a linear low density polyethylene or a low density polyethylene; and at least one second layer incorporating a linear low density polyethylene copolymer and optionally, a propylene-based copolymer and/or a low density polyethylene. Alternatively the second layer of the film structures may contain an in-reactor blend of a substantially linear polyethylene (or a homogeneously branched linear polyethylene) and a linear low density polyethylene. The film structures show an excellent balance of Dart impact, Elmendorf tear (in both the machine direction and cross direction), elastic holding force and elastic recovery.