A plant for storing energy by means of compressed air, in which: a storage volume accommodates air at elevated pressure pH; for energy storage, ambient air is compressed and introduced into the storage volume; for removal from storage, compressed air is extracted from the storage volume and discharged into the environment, performing work; at least one low-pressure turbomachine for alternate compression and expansion respectively compresses ambient air to a medium pressure pM and expands said ambient air from said pressure; at least one high-pressure machine for alternate compression and expansion respectively compresses air from the medium pressure pM to the store pressure pH and expands said air from the latter pressure; and said low-pressure turbomachine and high-pressure machine are connected in series in terms of flow and are mechanically coupled to in each case one, or to one common, electric machine that operates selectively as a motor and generator.