New shallow acceptor magnetoabsorption lines in THz range have been discovered under bandgap photoexcitation in strained Ge/GeSi multiple--quantum-well heterostructures. It is shown, both theoretically and experimentally, that the resonant absorption results from the photoionization of A + -centers and from 1s → 2p + -type transitions from the ground state of the barrier-situated A 0 -centers into excited states in the 1st and 2nd electronic subbands. The shallowest discovered ground acceptor states (E B ≤ 0.5 meV) are attributed to the "barrier-spaced" acceptors (a hole bound with an acceptor ion in the neighboring Ge quantum well).