A disposable garment or diaper having a fastener including fastener portions adapted for releasably mechanically engaging each other; and a bonding layer of room-temperature non-tacky thermoplastic material adhering one of the fastener portions to a thin polyolefin layer of the garment and being bonded to that polyolefin layer under heat and pressure that leaves the polyolefin layer substantially undeformed. The bonding layer holds the fastener portion to the polyolefin film with greater force than that which is required to separate the engaged fastener so that the fastener may be repetitively closed and opened.