Substantial field-dependent microwave absorption is found in superconducting materials of the YBa2Cu3O7 class. Abrupt changes occur over a 20-G range at zero field which are qualitatively different for polycrystalline and single-crystal materials. A strong hysteresis in polycrystalline samples is quenched by modulation fields of 0.2 Gpp. Formally the dissipative processes observed may be described in terms of flux relaxation, but the underlying physical mechanisms remain unresolved. As measurements on 100 g specimens can be performed in a few seconds, this property may prove useful for material characterization.