NOVELTY - Cyclic separation process for selectively separating hydrogen sulfide from a gas mixture which also comprises carbon dioxide, comprises contacting a stream of the gas mixture with a solution of a capped alkanolamine hydrogen sulfide absorbent or with a solution of sterically hindered secondary or tertiary amine hydrogen sulfide absorbent at a pressure of at least 1 bara.    USE - The processes are useful for selectively separating hydrogen sulfide from gas mixture also comprising carbon dioxide and increasing the selectivity of alkanolamine absorption process for hydrogen sulfide absorption from the gas mixture (claimed).    ADVANTAGE - The processes are performed at higher pressures by utilizing the capped alkanolamine hydrogen sulfide absorbent that rapidly reacts with hydrogen sulfide without being substantially displaced by reaction with carbon dioxide, thus enabling selectivity for hydrogen sulfide separation relative to carbon dioxide in the gas mixture, while maintaining very low carbon dioxide solubility, hence economical and energy efficient, and saves time.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are also included for:    (1) increasing the selectivity of an alkanolamine absorption process for hydrogen sulfide absorption from a gas mixture comprising carbon dioxide, comprising contacting a stream of the gas mixture with a solution of a capped alkanolamine hydrogen sulfide absorbent having at least one capped hydroxy group at a pressure of at least 1 bara; and    (2) an alkanolamine separation process or cyclic separation process for a natural gas stream containing hydrogen sulfide and carbon monoxide with improved selectivity for hydrogen sulfide separation relative to carbon dioxide separation at high pressures under conditions approaching absorbed hydrogen sulfide/carbon monoxide equilibrium, comprising contacting the natural gas stream in an absorption zone with a liquid solution of a sterically hindered capped alkanolamine or with a non-aqueous liquid solution of a sterically hindered secondary or tertiary amine to absorb hydrogen sulfide preferentially over carbon dioxide and form a rich stream of the absorbed hydrogen sulfide in the alkanolamine solution, passing the rich stream from the absorption zone to at least one regeneration zone and desorbing the absorbed hydrogen sulfide as gas from the alkanolamine solution or amine solution to form a lean solution containing a reduced concentration of absorbed hydrogen sulfide relative to the rich stream, and returning the lean stream to the absorption zone.