We present that the time structure of ZF- and LF-mu SR spectra in the magnetic phase of Sr2.5Ca11.5Cu24O41 and in the A-phase of Ce0.99Cu2.02Si2 shares a number of common features. In particular, the magnitude of local magnetic field at the muon site estimated from ZF-mu SR is seemingly far smaller than that estimated by LF-quenching experiment. As a microscopic model of such an anomalous local magnetic shielding, we discuss the possibility of muon-induced local magnetism due to the magnetic instability of frustrated spin systems near the quantum critical point. (C) 2000 Elsevier Science B.V. All rights reserved.