The microwave surface impedance of the high-Tc oxide superconductors has been measured at many laboratories around the world. A survey of their data between 100 MHz and 150 GHz for polycrystalline as well as single crystalline samples is given, focusing on YBa2Cu3O7-δ. In comparison to the classical superconductors, these results reveal a very similar temperature dependence of the surface impedance close to Tc but an anomalous high residual surface resistance at lower temperatures. Both features can be explained by the assumption that oxide superconductors contain a significant number of nonpairing charge carriers. Within the framework of a properly extended two-fluid model, this is shown by analysis of our best thin-film data. Moreover, the enhanced losses in polycrystalline material especially for superposed magnetostatic fields result, to a large extent, from the deeper penetration depth. The possible origin of the nonpairing charge carriers and their impact on the applicability of the oxide superconductors is briefly discussed. © 1990 Plenum Publishing Corporation.