A novel process for abatement of hydrogen sulphide from gas streams has been introduced, based on the combined action of a chemical absorption step and a biological oxidation step exploiting the biocatalytic ability of the bacterium Thiobacillus ferrooxidans. In this paper the process is discussed comprehensively, considering its double-stage version, which appeared as the more reliable. In the former stage (chemical step) H2S is absorbed in a ferric solution. In the second one (biological step) ferrous ion in the solution is oxidized by the biological action of Thiobacillus ferrooxidans. H2S is definitely converted to sulphur in a closed-reaction cycle. Kinetics of biooxidation and absorption with chemical reaction are discussed both on a theoretical basis and examining results of experiments performed in a lab-scale reactor system with fixed-bed bioreactor and bubble column absorber. Performance of the system is evaluated and kinetic models are proposed for the two steps, also including previous findings from the authors and other researchers.