  The recent report of superconductivity under high pressure at the record
transition temperature of Tc=203K in sulfur hydride has been identified as
conventional in view of the observation of an isotope effect upon deuteration.
Here it is demonstrated that conventional theories of superconductivity in the
sense of BCS or Eliashberg formalisms can neither account for the observed
values of Tc nor the pressure dependence of the isotope coefficient. The only
way out of the dilemma is a multi-band approach of superconductivity where
already small interband coupling suffices to achieve the high values of Tc
together with the anomalous pressure dependent isotope effect. In addition, it
is shown that anharmonicity of the hydrogen bonds vanishes under pressure
whereas anharmonic phonon modes related to sulfur are still active
