Dynamic resistance leads to the demagnetization of high-T c superconducting (HTS) permanent magnets (such as closed-loop coils and tape stacks) when exposed to AC fields. This letter reports on the systematic study of an unexpected dynamic resistance occurring in first cycle AC field, which can be induced by any weak AC field—even below the threshold value ‘conventionally’ defined for generating dynamic resistance. This resistance is predicted by a critical-state analytical calculation, and its physical origin is shown to be from the asymmetrical flux penetration. Numerically, this resistance is verified, and simulated for a closed-loop HTS coil, showing a non-negligible demagnetization effect. Experimentally, the current decay (i.e. demagnetization) characteristics of a closed-loop HTS coil in a sufficient range of AC fields are measured. This resistance manifests itself in the closed-loop coil as a relatively sharp current decay in the first cycle of the applied field; this observation is in qualitative agreement with the simulation. A comparative experiment is performed to eliminate the contribution from the index loss or ‘conventional’ dynamic resistance that also possibly results in a greater demagnetization in the first cycle owing to the larger coil current. As the result, this unexpected dynamic resistance is verified. The unexpected, sharp demagnetization caused by this resistance might need to be considered when designing HTS closed-loop coil applications.