Abstract: An inhaler (10) of the multiple single-dose type for administering doses of medicament in very fine or micronized powder form contained in blisters (30) in a blister sheet (60) comprises means (18) for bringing the blisters (30) of the blister sheet one after another into a piercing position, means (62) for piercing the individual blister, a delivery channel through which the patient exerts the inhalation action, and an air intake which communicates with the delivery channel (82) when a blister has been pierced. The blister sheet (60) is in the form of a strip with the blisters (30) aligned. A connection channel (22) is provided to connect the delivery channel (82) to the air intake (28). The blister (30) when in its piercing position is interposed between the delivery channel (82) and the connection channel (22). In this latter there is provided a cup (46) coaxial with the connection channel (22) and with its concavity facing the blister in the piercing position.