The present invention relates to pharmaceutical aerosols comprising a β-hairpin peptidomimetic of formula cyclo(-OctG-Glu-Thr-Ala-Ser-Ile-Pro-Pro-Gln-Lys-Tyr-DPro-Pro-), or a pharmaceutically acceptable salt thereof, having inhibitory activity against human neutrophil elastase. It further relates to solid or liquid pharmaceutical compositions and kits for preparing and administering such aerosols. The invention can be used for the prevention, management or treatment of pulmonary diseases, such as alpha-1 antitrypsin deficiency (AATD), cystic fibrosis (CF), non-cystic fibrosis bronchiactasis (NCFB), or chronic obstructive pulmonary disease (COPD), or infections, or diseases, or conditions of the lungs, being mediated by or resulting from human neutrophil elastase activity. Thus, the invention further relates to a pharmaceutical composition or a pharmaceutical aerosol comprising the active compound cyclo(-OctG-Glu-Thr-Ala-Ser-Ile-Pro-Pro-Gln-Lys-Tyr-DPro-Pro-), or any pharmaceutically acceptable salt thereof, for use in a method for the prevention, management or treatment of diseases or conditions of the lungs being mediated by or resulting from human neutrophil elastase activity in a subject.